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2 The term commercial mathematics is a combination of two words, commerce and math. Commerce relates to the concept of trade, business, etc., whereas mathematics deals with the calculation and analysis of these concepts. In this article, we will explore the idea of commercial mathematics.

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4 Math

5 Math Calculators

6 Math Formulas

7 Math Worksheets

8 <h2>What is Commercial Mathematics?</h2>

9 Commercial<a>math</a>is the branch<a>of</a>mathematics that focus on the calculation of profits,<a>discounts</a>,<a>taxes</a>, percentages, and many others<a>terms</a>related to<a>money</a>. It was first developed in the early 3rd millennium BCE in the Mesopotamian and Egyptian civilizations for trade and commerce.

10 The use of commercial mathematics in today's world is mainly related to the banking and financial sectors. The term “commercial” itself refers to business, trade, or activities intended to generate a<a>profit</a>.

11 <h2>Importance of Commercial Math</h2>

12 Commercial math is mainly used in the banking and finance sectors, as it deals with trade and commerce-related subjects. Even though banking and financial sectors are major users of commercial math, it is not limited to them. The main<a>functions</a>of commercial math:

13 <ol><li>Calculating profit and losses </li>

14 <li>Calculating monthly EMI, loans, and interest rates </li>

15 <li>Accurate calculations of taxes </li>

16 <li>Budgeting purposes </li>

17 <li>Investments and savings </li>

18 </ol><h2>Key Topics in Commercial Math</h2>

19 Since we have already discussed the primary uses and the definition of commercial mathematics, let us discuss the essential topics in commercial mathematics:

20 <ul><li><a>Profit and loss</a> </li>

21 <li><a>Simple interest</a> </li>

22 <li>Compound interest </li>

23 <li>Discounts </li>

24 <li>Taxes </li>

25 <li>Ratio and<a>proportion</a> </li>

26 <li>Partnerships </li>

27 <li>Time and work </li>

28 <li>Time, speed, and distance</li>

29 </ul><h3>Explore Our Programs</h3>

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31 <h3>Profit and Loss</h3>

30 <h3>Profit and Loss</h3>

32 All businesses work on the basic principle of profit and loss. Business can be simply defined as the act of conducting trade, and in trade, there is either a profit or a loss.

31 All businesses work on the basic principle of profit and loss. Business can be simply defined as the act of conducting trade, and in trade, there is either a profit or a loss.

33 What is profit?

32 What is profit?

34 Profit is the money a business retains after paying all its expenses. It is an important performance metric to understand the business’s financial gains. Profit is the value remaining after reducing the selling price from the cost price. The mathematical<a>expression</a>for profit is given by:

33 Profit is the money a business retains after paying all its expenses. It is an important performance metric to understand the business’s financial gains. Profit is the value remaining after reducing the selling price from the cost price. The mathematical<a>expression</a>for profit is given by:

35 Profit = Selling price - Cost price

34 Profit = Selling price - Cost price

36 Let us see how to calculate a<a>percentage</a>of profit. To find out how much profit was made compared to the cost, we use the<a>formula</a>for percentage as;

35 Let us see how to calculate a<a>percentage</a>of profit. To find out how much profit was made compared to the cost, we use the<a>formula</a>for percentage as;

37 Profit percentage =$ \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 $

36 Profit percentage =$ \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 $

38 Percentage change: The<a>percentage change</a>in profit shows how much profit has increased or decreased over time, expressed as a percentage of the original profit.

37 Percentage change: The<a>percentage change</a>in profit shows how much profit has increased or decreased over time, expressed as a percentage of the original profit.

39 $\text{Percentage Change in Profit}=\frac{New \ Profit-Old \ Profit }{Old \ Profit}×100%$

38 $\text{Percentage Change in Profit}=\frac{New \ Profit-Old \ Profit }{Old \ Profit}×100%$

40 What is loss?

39 What is loss?

41 When a<a>product</a>is sold for an amount<a>less than</a>the original cost, it is said to be a loss. The formula for calculating loss is expressed as:

40 When a<a>product</a>is sold for an amount<a>less than</a>the original cost, it is said to be a loss. The formula for calculating loss is expressed as:

42 $\text{Loss} = \text{cost price} - \text{selling price}$

41 $\text{Loss} = \text{cost price} - \text{selling price}$

43 Let's understand these terms using an example.

42 Let's understand these terms using an example.

44 Example:We bought a toy for ₹160 and sold it for ₹200. What percentage of profit did we make?

43 Example:We bought a toy for ₹160 and sold it for ₹200. What percentage of profit did we make?

45 Cost Price (CP) = ₹160

44 Cost Price (CP) = ₹160

46 Selling Price (SP) = ₹200

45 Selling Price (SP) = ₹200

47 <ol><li>Calculating profit:$\text{ Profit}= SP - CP$

46 <ol><li>Calculating profit:$\text{ Profit}= SP - CP$

48 $\text{ Profit} = 200 - 160 \\[1em] \text{ Profit}=₹40$

47 $\text{ Profit} = 200 - 160 \\[1em] \text{ Profit}=₹40$

49 </li>

48 </li>

50 <li>Now let's calculate the percentage of the profit we made:$\text{Profit Percentage } = \left( \frac{40}{160} \right) \times 100\\[1em] \text{Profit Percentage } = 25 \% $

49 <li>Now let's calculate the percentage of the profit we made:$\text{Profit Percentage } = \left( \frac{40}{160} \right) \times 100\\[1em] \text{Profit Percentage } = 25 \% $

51 </li>

50 </li>

52 </ol>Therefore, we made a profit of 25%.

51 </ol>Therefore, we made a profit of 25%.

53 <h3>Simple Interest</h3>

52 <h3>Simple Interest</h3>

54 Simple interest is the interest added or the extra money that is to be paid while returning borrowed money. It is only applicable on the original amount of money borrowed.

53 Simple interest is the interest added or the extra money that is to be paid while returning borrowed money. It is only applicable on the original amount of money borrowed.

55 Simple interest depends on three<a>factors</a>:

54 Simple interest depends on three<a>factors</a>:

56 <ol><li>Principal (P):It is the amount of money borrowed before any interest is added. </li>

55 <ol><li>Principal (P):It is the amount of money borrowed before any interest is added. </li>

57 <li>Rate (R):The<a>rate</a>of interest is the percentage of the principal amount that is paid or earned as interest per unit of time, usually per year. </li>

56 <li>Rate (R):The<a>rate</a>of interest is the percentage of the principal amount that is paid or earned as interest per unit of time, usually per year. </li>

58 <li>Time (T):The amount of time the money is borrowed or lent for in years or months.</li>

57 <li>Time (T):The amount of time the money is borrowed or lent for in years or months.</li>

59 </ol>So using these factors we have a formula to calculate the<a>simple interest</a>. The simple interest formula can be given as;

58 </ol>So using these factors we have a formula to calculate the<a>simple interest</a>. The simple interest formula can be given as;

60 $\text{Simple interest (SI)} = {{P \times T\times R} \over 100}$

59 $\text{Simple interest (SI)} = {{P \times T\times R} \over 100}$

61 We can use this formula to calculate simple interest. Now, let's use an example to understand what simple interest is and how it works.

60 We can use this formula to calculate simple interest. Now, let's use an example to understand what simple interest is and how it works.

62 Example:A person borrowed Rs 5000 and promised to pay the bank back in 3 years with a 5% interest per year. Calculate the simple interest.

61 Example:A person borrowed Rs 5000 and promised to pay the bank back in 3 years with a 5% interest per year. Calculate the simple interest.

63 <ul><li>Step 1:We identify the values$Principal = ₹5000$

62 <ul><li>Step 1:We identify the values$Principal = ₹5000$

64 $Rate = 5\%$

63 $Rate = 5\%$

65 $Time = 3 \ years$

64 $Time = 3 \ years$

66 </li>

65 </li>

67 <li>Step 2:Calculate using the formula$SI = \frac {5000 \space \times \space5 \space × \space3}{100}$

66 <li>Step 2:Calculate using the formula$SI = \frac {5000 \space \times \space5 \space × \space3}{100}$

68 $SI = {75000 \over 100} = ₹750$

67 $SI = {75000 \over 100} = ₹750$

69 Therefore, after 3 years you will earn, ₹750 as interest.

68 Therefore, after 3 years you will earn, ₹750 as interest.

70 </li>

69 </li>

71 <li>So the total money you will earn is:$5000 + 750 = ₹5750$

70 <li>So the total money you will earn is:$5000 + 750 = ₹5750$

72 </li>

71 </li>

73 </ul><h3>Compound Interest</h3>

72 </ul><h3>Compound Interest</h3>

74 The interest earned on both the original amount and the interest that has already been added is called<a>compound interest</a>.

73 The interest earned on both the original amount and the interest that has already been added is called<a>compound interest</a>.

75 Compound interest can be calculated using:

74 Compound interest can be calculated using:

76 <ul><li>Principal (P):The initial amount of money </li>

75 <ul><li>Principal (P):The initial amount of money </li>

77 <li>Amount (A):Total amount of money you will earn </li>

76 <li>Amount (A):Total amount of money you will earn </li>

78 <li>Rate (R):The percentage of interest you would earn </li>

77 <li>Rate (R):The percentage of interest you would earn </li>

79 <li>n:The total<a>number</a>of times the interest is compounded in a given year </li>

78 <li>n:The total<a>number</a>of times the interest is compounded in a given year </li>

80 <li>T:Time in years</li>

79 <li>T:Time in years</li>

81 </ul>So there are two formulas for calculating the amount:

80 </ul>So there are two formulas for calculating the amount:

82 <ol><li>Compounded annually: $ A = P (1 + \frac{R}{100})^T $

81 <ol><li>Compounded annually: $ A = P (1 + \frac{R}{100})^T $

83 </li>

82 </li>

84 <li>Frequent compounding (quarterly, monthly, etc.): $A = P(1 + \frac{r} {n})^{nT}$

83 <li>Frequent compounding (quarterly, monthly, etc.): $A = P(1 + \frac{r} {n})^{nT}$

85 </li>

84 </li>

86 </ol>Now, after finding the amount, compound interest can be calculated by using formula:

85 </ol>Now, after finding the amount, compound interest can be calculated by using formula:

87 $\text{Compound Interest = Amount - Principal}$

86 $\text{Compound Interest = Amount - Principal}$

88 Here are a few examples that use these formulas:

87 Here are a few examples that use these formulas:

89 Example 1:Rohan put ₹ 1500 in the bank at 15% interest per year, compounded quarterly, for two years. Find the compound interest.

88 Example 1:Rohan put ₹ 1500 in the bank at 15% interest per year, compounded quarterly, for two years. Find the compound interest.

90 <ul><li>Step 1:Identify the valuesP = 1500

89 <ul><li>Step 1:Identify the valuesP = 1500

91 n = 4 (because it's compounded quarterly)

90 n = 4 (because it's compounded quarterly)

92 T = 2

91 T = 2

93 </li>

92 </li>

94 </ul><ul><li>Step 2:Use the compound quarterly formula:$A = P(1 + \frac{r} {n})^{nT}$

93 </ul><ul><li>Step 2:Use the compound quarterly formula:$A = P(1 + \frac{r} {n})^{nT}$

95 $A = 1500(1 + \frac{0.15} {4})^{4 \times 2}$

94 $A = 1500(1 + \frac{0.15} {4})^{4 \times 2}$

96 $A = 1500 (1.0375)^8$

95 $A = 1500 (1.0375)^8$

97 $A = 1500 (1.3425) \\[1em] A= 2013.75$

96 $A = 1500 (1.3425) \\[1em] A= 2013.75$

98 </li>

97 </li>

99 </ul><ul><li>Compound interest:$\text{Compound Interest} = A - P \\[1em] \text{Compound Interest}= 2013.75 - 1500\\[1em] \text{Compound Interest}= ₹ 513.75$

98 </ul><ul><li>Compound interest:$\text{Compound Interest} = A - P \\[1em] \text{Compound Interest}= 2013.75 - 1500\\[1em] \text{Compound Interest}= ₹ 513.75$

100 </li>

99 </li>

101 </ul>Example 2:Now Rohan put ₹3000 in the bank at 12% interest per year, compounded annually, for three years. Find the compound interest.

100 </ul>Example 2:Now Rohan put ₹3000 in the bank at 12% interest per year, compounded annually, for three years. Find the compound interest.

102 <ul><li>Step 1:Identify the valuesP = 3000

101 <ul><li>Step 1:Identify the valuesP = 3000

103 R = 12%

102 R = 12%

104 T = 3

103 T = 3

105 </li>

104 </li>

106 </ul><ul><li>Step 2:Calculating amount using the compounded annual formula:$ A = P (1 + \frac{R}{100})^T $

105 </ul><ul><li>Step 2:Calculating amount using the compounded annual formula:$ A = P (1 + \frac{R}{100})^T $

107 $ A = 3000 (1 + \frac{12}{100})^3 $$ A = 3000 (1.12)^3$

106 $ A = 3000 (1 + \frac{12}{100})^3 $$ A = 3000 (1.12)^3$

108 $ A = 3000 (1.404928)$

107 $ A = 3000 (1.404928)$

109 $A = ₹4214.784$

108 $A = ₹4214.784$

110 </li>

109 </li>

111 <li>Calculating compound interest:

110 <li>Calculating compound interest:

112 $\text {Compound Interest} = 4214.784 - 3000 \\[1em] \text {Compound Interest}= ₹1214.784$

111 $\text {Compound Interest} = 4214.784 - 3000 \\[1em] \text {Compound Interest}= ₹1214.784$

113 </li>

112 </li>

114 </ul>Simple interest Vs Compound interest

113 </ul>Simple interest Vs Compound interest

115 The following table gives the differences between simple interest and compound interest.

114 The following table gives the differences between simple interest and compound interest.

116 Simple interest Compound interestSimple Interest is the extra money you earn, or you have to pay, on the original amount over a fixed period of time.

115 Simple interest Compound interestSimple Interest is the extra money you earn, or you have to pay, on the original amount over a fixed period of time.

117 Compound interest is when the interest accumulates and compounds over the principal amount over a certain period of time.

116 Compound interest is when the interest accumulates and compounds over the principal amount over a certain period of time.

118 SI is calculated only on the principal amount. CI is calculated both on the principal and the previously earned interest. Return is less. Return is higher. The principal amount always remains<a>constant</a>. Principal amount can keep varying during the time period.<h3>Discounts</h3>

117 SI is calculated only on the principal amount. CI is calculated both on the principal and the previously earned interest. Return is less. Return is higher. The principal amount always remains<a>constant</a>. Principal amount can keep varying during the time period.<h3>Discounts</h3>

119 A reduction in the price of an object or a<a>set</a>of objects is called a discount. It is a widely used technique employed by businesspeople to attract both existing and new customers. A discount can be expressed as a percentage reduction or as a flat money discount.

118 A reduction in the price of an object or a<a>set</a>of objects is called a discount. It is a widely used technique employed by businesspeople to attract both existing and new customers. A discount can be expressed as a percentage reduction or as a flat money discount.

120 We use the following formula to calculate the discount:

119 We use the following formula to calculate the discount:

121 <ul><li>$\text{Discount} = \text{Marked Price} - \text{Selling Price}$ </li>

120 <ul><li>$\text{Discount} = \text{Marked Price} - \text{Selling Price}$ </li>

122 <li>$\text{Discount percentage} = \frac{\text {Discount}} {\text{Marked Price}} \times 100$</li>

121 <li>$\text{Discount percentage} = \frac{\text {Discount}} {\text{Marked Price}} \times 100$</li>

123 </ul>Percentage difference: The percentage difference measures how much two numbers differ from each other as a percentage of their<a>average</a>. To calculate percentage difference, we use the percentage formula:

122 </ul>Percentage difference: The percentage difference measures how much two numbers differ from each other as a percentage of their<a>average</a>. To calculate percentage difference, we use the percentage formula:

124 $\text{Percentage Difference}=\frac{∣A-B∣ }{\frac{(A+B)}{2}} ×100%$

123 $\text{Percentage Difference}=\frac{∣A-B∣ }{\frac{(A+B)}{2}} ×100%$

125 Discount rate:The discount rate is the percentage reduction applied to the original (list) price of an item.

124 Discount rate:The discount rate is the percentage reduction applied to the original (list) price of an item.

126 We can calculate the discount rate by using the formula;

125 We can calculate the discount rate by using the formula;

127 $\text{Discount Rate}=\frac{\text{Discount Amount}}{\text{Original Price}} ×100\%$

126 $\text{Discount Rate}=\frac{\text{Discount Amount}}{\text{Original Price}} ×100\%$

128 Calculating a discount is done in two cases:

127 Calculating a discount is done in two cases:

129 When the marked price and selling price are both given, we use the discount formula, which is calculated by subtracting the selling price from the marked price. Another case is when the discount percentage is given, we use the discount percentage formula.

128 When the marked price and selling price are both given, we use the discount formula, which is calculated by subtracting the selling price from the marked price. Another case is when the discount percentage is given, we use the discount percentage formula.

130 Let's use these formulas in real-life examples to get a better understanding:

129 Let's use these formulas in real-life examples to get a better understanding:

131 Example:A PlayStation 5 costs around $450, but it is being sold for $360. Find the discount amount and the discount percentage.

130 Example:A PlayStation 5 costs around $450, but it is being sold for $360. Find the discount amount and the discount percentage.

132 Given:

131 Given:

133 Marked Price = $450

132 Marked Price = $450

134 Selling Price = $360

133 Selling Price = $360

135 <ul><li>Step 1:We calculate the discount amount$\text{Discount} = \text{Marked Price} - \text{Selling Price}$

134 <ul><li>Step 1:We calculate the discount amount$\text{Discount} = \text{Marked Price} - \text{Selling Price}$

136 $\text{Discount} = 450 - 360 \\[1em] \text{Discount} = $90$

135 $\text{Discount} = 450 - 360 \\[1em] \text{Discount} = $90$

137 </li>

136 </li>

138 </ul><ul><li>Step 2:Now that we have the discount amount, we find the discount percentage.$\text{Discount percentage} = \frac{{90}} {450} \times 100 \\[1em] \text{Discount percentage}= 20 \%$

137 </ul><ul><li>Step 2:Now that we have the discount amount, we find the discount percentage.$\text{Discount percentage} = \frac{{90}} {450} \times 100 \\[1em] \text{Discount percentage}= 20 \%$

139 </li>

138 </li>

140 </ul>So there is a 20% discount on the PlayStation 5.

139 </ul>So there is a 20% discount on the PlayStation 5.

141 <h3>Taxes</h3>

140 <h3>Taxes</h3>

142 Tax is the amount of money that is collected from eligible individuals and organizations that are liable to pay and is transferred to the government. The money is used for the development and welfare of the country.

141 Tax is the amount of money that is collected from eligible individuals and organizations that are liable to pay and is transferred to the government. The money is used for the development and welfare of the country.

143 A formula used to calculate tax is:

142 A formula used to calculate tax is:

144 $\text{Tax amount} = \text {Selling Price} \times {{{\text{Tax Rate}} \over 100}}$

143 $\text{Tax amount} = \text {Selling Price} \times {{{\text{Tax Rate}} \over 100}}$

145 There are two types of taxes :

144 There are two types of taxes :

146 Direct tax- These are paid directly to the government, like when you get your salary a small portion of it goes to the government.

145 Direct tax- These are paid directly to the government, like when you get your salary a small portion of it goes to the government.

147 Indirect tax- These taxes are paid to businesses, which then pays the government. Sales tax is an example of indirect tax.

146 Indirect tax- These taxes are paid to businesses, which then pays the government. Sales tax is an example of indirect tax.

148 What is GST?

147 What is GST?

149 Goods and Services Tax (GST) is the price that is added to various products and services that are bought and sold. This is then collected by the government, which would be used for public.

148 Goods and Services Tax (GST) is the price that is added to various products and services that are bought and sold. This is then collected by the government, which would be used for public.

150 GST has formulas of its own as well. The formulas are:

149 GST has formulas of its own as well. The formulas are:

151 <ul><li>$\text{GST Amount} = {\frac{\text{GST %} \space \times \space \text{Price}}{100} }$ </li>

150 <ul><li>$\text{GST Amount} = {\frac{\text{GST %} \space \times \space \text{Price}}{100} }$ </li>

152 <li>$\text{Final Price} = \text{Price} \times \big( {1 + \frac{\text{GST%}}{100} }\big)$</li>

151 <li>$\text{Final Price} = \text{Price} \times \big( {1 + \frac{\text{GST%}}{100} }\big)$</li>

153 </ul>Let's use these in some examples

152 </ul>Let's use these in some examples

154 Example 1:You buy a shirt that costs you around ₹500, the GST rate is 13%. Find the total amount after GST.

153 Example 1:You buy a shirt that costs you around ₹500, the GST rate is 13%. Find the total amount after GST.

155 Given:

154 Given:

156 GST = 13%

155 GST = 13%

157 Price = ₹500

156 Price = ₹500

158 <ul><li>Step 1:Find the GST amount:$\text{GST Amount} = {\frac{\text{GST %} \space \times \space \text{Price}}{100} }$

157 <ul><li>Step 1:Find the GST amount:$\text{GST Amount} = {\frac{\text{GST %} \space \times \space \text{Price}}{100} }$

159 $\text{GST Amount }= \frac{13 \space \times \space500}{100} \\[1em] \text{GST Amount }= ₹65$

158 $\text{GST Amount }= \frac{13 \space \times \space500}{100} \\[1em] \text{GST Amount }= ₹65$

160 </li>

159 </li>

161 </ul><ul><li>Step 2:Find the final price$\text{Final price} = 500 + 65 = ₹565$

160 </ul><ul><li>Step 2:Find the final price$\text{Final price} = 500 + 65 = ₹565$

162 </li>

161 </li>

163 </ul>So the price of the shirt after GST is ₹565.

162 </ul>So the price of the shirt after GST is ₹565.

164 <h3>Ratio and Proportion</h3>

163 <h3>Ratio and Proportion</h3>

165 <a>Ratio</a>is a way of<a>comparing</a>two quantities, whereas proportion states the equality of two<a>ratios</a>. The<a>concept of ratio</a>and proportion is widely used in daily life as well as in commerce and science.

164 <a>Ratio</a>is a way of<a>comparing</a>two quantities, whereas proportion states the equality of two<a>ratios</a>. The<a>concept of ratio</a>and proportion is widely used in daily life as well as in commerce and science.

166 What is ratio?

165 What is ratio?

167 Two quantities compared with each other is what we call ratio. It tells us how much one thing is compared to another.

166 Two quantities compared with each other is what we call ratio. It tells us how much one thing is compared to another.

168 We write ratio as:

167 We write ratio as:

169 a:b (we read it is ‘a' is to b’)

168 a:b (we read it is ‘a' is to b’)

170 Example 1:We mix 2 cups of milk with 3 cups of water. What is the ratio?

169 Example 1:We mix 2 cups of milk with 3 cups of water. What is the ratio?

171 Solution:The ratio is 2:3

170 Solution:The ratio is 2:3

172 This means that for every 2 cups of milk, there will be 3 cups of water.

171 This means that for every 2 cups of milk, there will be 3 cups of water.

173 What is proportion?

172 What is proportion?

174 <a>Proportions</a>is a concept of showing if two values are in ratio or not.

173 <a>Proportions</a>is a concept of showing if two values are in ratio or not.

175 We write proportion as:

174 We write proportion as:

176 ${{a} \over b}= {{c} \over d}$

175 ${{a} \over b}= {{c} \over d}$

177 Example 2:If 2 cups of sugar is added to 4 cups of milk, then how many cups of sugar is required for 8 cups of milk?

176 Example 2:If 2 cups of sugar is added to 4 cups of milk, then how many cups of sugar is required for 8 cups of milk?

178 Solution: ${{2} \over 4}$ = $ {{x} \over 8}$

177 Solution: ${{2} \over 4}$ = $ {{x} \over 8}$

179 Now we solve for x by cross-multiplying:

178 Now we solve for x by cross-multiplying:

180 $ 2 \times 8 = 4 \times x \\ \space \\ 16 = 4x \\ \space \\ x = \frac{16}{4} \\ \space \\ x = 4 $

179 $ 2 \times 8 = 4 \times x \\ \space \\ 16 = 4x \\ \space \\ x = \frac{16}{4} \\ \space \\ x = 4 $

181 So 4 cups of sugar are needed for 8 cups of milk.

180 So 4 cups of sugar are needed for 8 cups of milk.

182 <h3>Partnerships</h3>

181 <h3>Partnerships</h3>

183 Two people coming together and starting a business arrangement, sharing the profit and losses, is what we call a partnership.

182 Two people coming together and starting a business arrangement, sharing the profit and losses, is what we call a partnership.

184 The amount of money a partner invests in the company decides how much profit or loss each partner gets. Usually, partnerships are formed among large companies like Ben & Jerry's or Apple.

183 The amount of money a partner invests in the company decides how much profit or loss each partner gets. Usually, partnerships are formed among large companies like Ben & Jerry's or Apple.

185 How are the profits shared between partners?

184 How are the profits shared between partners?

186 The distribution of profits among partners according to the investment made by each business partner is called profit-sharing.

185 The distribution of profits among partners according to the investment made by each business partner is called profit-sharing.

187 To calculate profit-sharing, the formula is given by:

186 To calculate profit-sharing, the formula is given by:

188 $\text{Partner's share} = \frac{\text{Partner's investment} \space \times \space \text{Total profit}}{\text{Total investment}} $

187 $\text{Partner's share} = \frac{\text{Partner's investment} \space \times \space \text{Total profit}}{\text{Total investment}} $

189 Example 1:So two partners Pam and Tam start a business. Pam invests $3000 and Tam invests $2000. The total profit is, $5000. Find out each partner’s share.

188 Example 1:So two partners Pam and Tam start a business. Pam invests $3000 and Tam invests $2000. The total profit is, $5000. Find out each partner’s share.

190 <ul><li>Step 1:Find the total investment$3000 + 2000 = $5000$</li>

189 <ul><li>Step 1:Find the total investment$3000 + 2000 = $5000$</li>

191 </ul><ul><li>Step 2:Calculate the shares $\text{Pam’s share } = \frac{3000 \space \times \space 5000}{5000} = $3000 $$\text{Tam’s share } = \frac{2000 \times 5000}{5000} = $2000 $

190 </ul><ul><li>Step 2:Calculate the shares $\text{Pam’s share } = \frac{3000 \space \times \space 5000}{5000} = $3000 $$\text{Tam’s share } = \frac{2000 \times 5000}{5000} = $2000 $

192 </li>

191 </li>

193 </ul>Final profit: Pam gets ₹3000 and Tam gets ₹2000.

192 </ul>Final profit: Pam gets ₹3000 and Tam gets ₹2000.

194 <h3>Time and Work</h3>

193 <h3>Time and Work</h3>

195 This topic is all about the amount of work done in a said time by a person or a group of people.

194 This topic is all about the amount of work done in a said time by a person or a group of people.

196 Here are some of the key points to remember:

195 Here are some of the key points to remember:

197 <ol><li>Work:Any given task that must be completed.

196 <ol><li>Work:Any given task that must be completed.

198 </li>

197 </li>

199 <li>Time:The number of minutes or hours taken to complete the said task. </li>

198 <li>Time:The number of minutes or hours taken to complete the said task. </li>

200 <li>Efficiency:The ability to complete the task correctly without spending too much time. </li>

199 <li>Efficiency:The ability to complete the task correctly without spending too much time. </li>

201 <li>Combined efficiency:The total efficiency of two or more people involved in a task. </li>

200 <li>Combined efficiency:The total efficiency of two or more people involved in a task. </li>

202 </ol>Some formulas for work and time are:

201 </ol>Some formulas for work and time are:

203 <ul><li>$\text{Work Done = Efficiency × Time}$ </li>

202 <ul><li>$\text{Work Done = Efficiency × Time}$ </li>

204 </ul><ul><li>$\text{Time} = \frac{\text{Work}}{\text{Efficiency}} $ </li>

203 </ul><ul><li>$\text{Time} = \frac{\text{Work}}{\text{Efficiency}} $ </li>

205 </ul><ul><li>$\text{Efficiency} = \frac{\text{Work}}{\text{Time}} $

204 </ul><ul><li>$\text{Efficiency} = \frac{\text{Work}}{\text{Time}} $

206 </li>

205 </li>

207 </ul><ul><li>$\text{Combined Efficiency} = \text{Efficiency}_1 + \text{Efficiency}_2 + ….. + \space \text{Efficiency}_n$ </li>

206 </ul><ul><li>$\text{Combined Efficiency} = \text{Efficiency}_1 + \text{Efficiency}_2 + ….. + \space \text{Efficiency}_n$ </li>

208 </ul><ul><li>Time taken by<a>multiple</a>workers: $\text{Time} = \frac{\text{Work}}{\text{Combined Efficiency}} $</li>

207 </ul><ul><li>Time taken by<a>multiple</a>workers: $\text{Time} = \frac{\text{Work}}{\text{Combined Efficiency}} $</li>

209 </ul>Let's understand this through an example

208 </ul>Let's understand this through an example

210 Example 1:Andy is a salesman who can complete his task in 10 days. How efficient is Andy in his work, and how much would he be able to complete in 4 days?

209 Example 1:Andy is a salesman who can complete his task in 10 days. How efficient is Andy in his work, and how much would he be able to complete in 4 days?

211 Solution:

210 Solution:

212 <ol><li>Calculating efficiency:$\text{Efficiency} = \frac{\text{Work}}{\text{Time}} $

211 <ol><li>Calculating efficiency:$\text{Efficiency} = \frac{\text{Work}}{\text{Time}} $

213 $⇒ \text{Total work} = 1\ \text{job}$

212 $⇒ \text{Total work} = 1\ \text{job}$

214 $⇒ \text{Time} = 10 \ \text{days}$

213 $⇒ \text{Time} = 10 \ \text{days}$

215 $\text{Efficiency} = \frac{\text{1}}{\text{10}} $

214 $\text{Efficiency} = \frac{\text{1}}{\text{10}} $

216 So, Andy completes $\frac{1}{10} $ of the work per day

215 So, Andy completes $\frac{1}{10} $ of the work per day

217 </li>

216 </li>

218 <li>Calculating work:$\text{Work Done = Efficiency × Time}$$⇒ \text{Efficiency} =\frac{1}{10} $

217 <li>Calculating work:$\text{Work Done = Efficiency × Time}$$⇒ \text{Efficiency} =\frac{1}{10} $

219 $ \text{Work} = \frac{1}{4} × 4 = 0.4 $

218 $ \text{Work} = \frac{1}{4} × 4 = 0.4 $

220 </li>

219 </li>

221 </ol>So, Andy’s efficiency is $\frac{1}{10} $ of the work per day, and in 4 days he will be able to complete only 40% of the work.

220 </ol>So, Andy’s efficiency is $\frac{1}{10} $ of the work per day, and in 4 days he will be able to complete only 40% of the work.

222 <h3>Time, Speed, and Distance</h3>

221 <h3>Time, Speed, and Distance</h3>

223 We use time, speed, and distance to understand how fast an object moves from point to another and how long it would take to get there.

222 We use time, speed, and distance to understand how fast an object moves from point to another and how long it would take to get there.

224 <ol><li>Time: It is the measure of the duration that is required to cover the distance between two points.Formula:$\text{Time} = \frac{\text{Distance}}{\text{Speed}} $

223 <ol><li>Time: It is the measure of the duration that is required to cover the distance between two points.Formula:$\text{Time} = \frac{\text{Distance}}{\text{Speed}} $

225 </li>

224 </li>

226 <li>Distance:the total length of path covered when travelling between two points.Formula: $\text{Distance = Speed × Time}$

225 <li>Distance:the total length of path covered when travelling between two points.Formula: $\text{Distance = Speed × Time}$

227 </li>

226 </li>

228 <li>Speed:The speed of an object is defined as the rate at which it travels a certain distance in a given period of time. Usually, speed is measured in kilometers per hour (km/h) or meters per second (m/s).Formula:$\text{Speed} = \frac{\text{Distance}}{\text{Time}} $

227 <li>Speed:The speed of an object is defined as the rate at which it travels a certain distance in a given period of time. Usually, speed is measured in kilometers per hour (km/h) or meters per second (m/s).Formula:$\text{Speed} = \frac{\text{Distance}}{\text{Time}} $

229 </li>

228 </li>

230 </ol>The following image provides a better visualization of time, distance and speed formula:

229 </ol>The following image provides a better visualization of time, distance and speed formula:

231 Let’s use these formulas in an example

230 Let’s use these formulas in an example

232 Example 1:A car is travelling from point A to point B at a speed of 60 km/h. How much time will it take to travel 180kms?

231 Example 1:A car is travelling from point A to point B at a speed of 60 km/h. How much time will it take to travel 180kms?

233 Solution:We will use the time formula:

232 Solution:We will use the time formula:

234 $\text{Time} = \frac{\text{Distance}}{\text{Speed}} $

233 $\text{Time} = \frac{\text{Distance}}{\text{Speed}} $

235 $\text{Time} = \frac{180}{60} $

234 $\text{Time} = \frac{180}{60} $

236 $\text{Time} = 3 \ \text{hours}$

235 $\text{Time} = 3 \ \text{hours}$

237 To travel 180kms, the car will take 3 hours at a speed of 60 km/h.

236 To travel 180kms, the car will take 3 hours at a speed of 60 km/h.

238 <h2>Tips and Tricks to Master Commercial Math</h2>

237 <h2>Tips and Tricks to Master Commercial Math</h2>

239 Learning commercial<a>math</a>can definitely feel overwhelming as there are a lot of formulas and concepts to learn. Here are some tips and tricks to know that will make studying these concepts much easier.

238 Learning commercial<a>math</a>can definitely feel overwhelming as there are a lot of formulas and concepts to learn. Here are some tips and tricks to know that will make studying these concepts much easier.

240 <ol><li>Memorize basic formulas. These formulas will help you avoid mistakes: a. Profit and loss:

239 <ol><li>Memorize basic formulas. These formulas will help you avoid mistakes: a. Profit and loss:

241 $\text{Profit = Selling price - Cost price}$

240 $\text{Profit = Selling price - Cost price}$

242 $\text{Loss = Cost price - Selling price}$

241 $\text{Loss = Cost price - Selling price}$

243 b.Simple interest:$SI = \frac{P \times R \times T}{100} $

242 b.Simple interest:$SI = \frac{P \times R \times T}{100} $

244 c. Time, Speed, and Distance:

243 c. Time, Speed, and Distance:

245 $Distance = speed × time$

244 $Distance = speed × time$

246 $\text{Speed} = \frac{\text{Distance}}{\text{Time}} $

245 $\text{Speed} = \frac{\text{Distance}}{\text{Time}} $

247 $\text{Time} = \frac{\text{Distance}}{\text{Speed}} $

246 $\text{Time} = \frac{\text{Distance}}{\text{Speed}} $

248 </li>

247 </li>

249 <li>Using percentage shortcuts for calculations can help you to solve problems faster:

248 <li>Using percentage shortcuts for calculations can help you to solve problems faster:

250 10% of a number: You just need to move the<a>decimal</a>point one place to its left. Example: 10% of 500 = 50

249 10% of a number: You just need to move the<a>decimal</a>point one place to its left. Example: 10% of 500 = 50

251 1% of a number: Over here, we have to just divide the number by 100. Example 1% of 3000 = 3000/100 = 30

250 1% of a number: Over here, we have to just divide the number by 100. Example 1% of 3000 = 3000/100 = 30

252 </li>

251 </li>

253 <li>Practice solving with real world examples: Using real world examples would definitely help you understand how formulas work.

252 <li>Practice solving with real world examples: Using real world examples would definitely help you understand how formulas work.

254 </li>

253 </li>

255 <li>Make sure to understand and apply ratios and proportions:Go step by step, simplify the ratios or<a>fractions</a>first and then<a>cross multiply</a>when it comes to solving for proportions.

254 <li>Make sure to understand and apply ratios and proportions:Go step by step, simplify the ratios or<a>fractions</a>first and then<a>cross multiply</a>when it comes to solving for proportions.

256 </li>

255 </li>

257 <li>Be careful about successive changes:In situations where there are multiple discounts or losses, it is essential to subtract or add accordingly based on the<a>question</a>. Not every time is the discount or loss applied to the original price.

256 <li>Be careful about successive changes:In situations where there are multiple discounts or losses, it is essential to subtract or add accordingly based on the<a>question</a>. Not every time is the discount or loss applied to the original price.

258 </li>

257 </li>

259 <li>Use everyday shopping:Parents should ask their kids while grocery shopping, or online shopping, “If this is 20% off, how much money do we save?” or ask them like, “Which deal is better: 25% off or ₹200 off?” Let kids use a<a>calculator</a>or phone to check. It would build their confidence.

258 <li>Use everyday shopping:Parents should ask their kids while grocery shopping, or online shopping, “If this is 20% off, how much money do we save?” or ask them like, “Which deal is better: 25% off or ₹200 off?” Let kids use a<a>calculator</a>or phone to check. It would build their confidence.

260 </li>

259 </li>

261 <li>Involve your kid in family budgeting:Parents should be showing how they are planning expenses and comparing costs. Ask your kid to calculate the amount of money that will be saved if you choose a cheaper option.

260 <li>Involve your kid in family budgeting:Parents should be showing how they are planning expenses and comparing costs. Ask your kid to calculate the amount of money that will be saved if you choose a cheaper option.

262 </li>

261 </li>

263 <li>Start with real-world context:Teachers should begin teaching the lessons with relatable examples. Some basic examples like shopping, the school canteen, or movie tickets. Try to ask them questions like “If our school canteen sells 50 sandwiches at ₹40 each, and it costs ₹30 to make them, what’s the profit?”

262 <li>Start with real-world context:Teachers should begin teaching the lessons with relatable examples. Some basic examples like shopping, the school canteen, or movie tickets. Try to ask them questions like “If our school canteen sells 50 sandwiches at ₹40 each, and it costs ₹30 to make them, what’s the profit?”

264 </li>

263 </li>

265 <li>Integrate role play:Make the students act as shopkeepers and customers. Give them price lists and let them compute total bills, discounts, and change.

264 <li>Integrate role play:Make the students act as shopkeepers and customers. Give them price lists and let them compute total bills, discounts, and change.

266 </li>

265 </li>

267 </ol><h2>Common Mistakes and How to Avoid Them in Commercial Math</h2>

266 </ol><h2>Common Mistakes and How to Avoid Them in Commercial Math</h2>

268 Making mistakes is common when learning commercial math. However, it can be avoided if the mistakes are identified well in advance. Some of them are mentioned here:

267 Making mistakes is common when learning commercial math. However, it can be avoided if the mistakes are identified well in advance. Some of them are mentioned here:

269 <h2>Real-Life Applications of Commercial Math</h2>

268 <h2>Real-Life Applications of Commercial Math</h2>

270 We need commercial math to calculate profit, losses, or discounts. Every business also needs to pay tax to the government.

269 We need commercial math to calculate profit, losses, or discounts. Every business also needs to pay tax to the government.

271 Here are some ways we apply Commercial Math in Real life:

270 Here are some ways we apply Commercial Math in Real life:

272 <ol><li>Businesses or startups: Commercial Math is very essential in running businesses. It is one of the first things that each business uses to calculate their profit and loss, their partnerships, basically anything needed to manage finances. </li>

271 <ol><li>Businesses or startups: Commercial Math is very essential in running businesses. It is one of the first things that each business uses to calculate their profit and loss, their partnerships, basically anything needed to manage finances. </li>

273 <li>Banking: Banks use commercial math mainly to manage transactions with their customers, and they also use it for loans. Simple interest and compound interests are a few things that banks use. </li>

272 <li>Banking: Banks use commercial math mainly to manage transactions with their customers, and they also use it for loans. Simple interest and compound interests are a few things that banks use. </li>

274 <li>Shopping and retail: Commercial Math is quite widely used in shopping and retail, especially when calculating how much we save in a discount or how much tax you would end up paying during a purchase. </li>

273 <li>Shopping and retail: Commercial Math is quite widely used in shopping and retail, especially when calculating how much we save in a discount or how much tax you would end up paying during a purchase. </li>

275 <li>Stocks and investing: We use compound interest, a concept in commercial math, to help us calculate our investments. </li>

274 <li>Stocks and investing: We use compound interest, a concept in commercial math, to help us calculate our investments. </li>

276 <li>Saving money: Commercial math is used as a tool in personal finance management. Calculations related to the amount of money that needs to be saved for future expenses are done through commercial math.</li>

275 <li>Saving money: Commercial math is used as a tool in personal finance management. Calculations related to the amount of money that needs to be saved for future expenses are done through commercial math.</li>

277 </ol>These are some of the few areas in our daily lives where commercial math is widely used.

276 </ol>These are some of the few areas in our daily lives where commercial math is widely used.

277 + <h2>Download Worksheets</h2>

278 <h3>Problem 1</h3>

279 Anil bought a bicycle for ₹1500. He then sold it for ₹1800. What is Anil’s profit? Also calculate the percentage of profit.

280 Okay, lets begin

281 Profit is ₹300

282 Profit percentage = 20%.

283 <h3>Explanation</h3>

284 $\text {Profit} = 1800 - 1500 = 300 \\ \space \\ \text {Profit} \% = \frac{300}{1500} × 100$

285 Anil earns a profit of 20%.

286 Well explained 👍

287 <h3>Problem 2</h3>

288 Find the compound interest on $15000 at 5% per year for 3 years.

289 Okay, lets begin

290 Compound interest is $2364.375

291 <h3>Explanation</h3>

292 <ol><li>Calculating Amount:$ A = P(1 + \frac{R}{100} )^T $

293 $ A = 1500(1 + \frac{5}{100} )^3 $

294 $A= 15000 (1.05)^3$

295 $A = 15000 (1.157625)$

296 $A = $17,364.375$

297 </li>

298 <li>Calculating CI$CI = A - P \\[1em] CI = 17364.375 - 15000 \\[1em] CI= $2364.375$

299 </li>

300 </ol>The compound interest is $2364.375

301 Well explained 👍

302 <h3>Problem 3</h3>

303 A dress costs around $2000 but is sold at a 20% discount. Find the selling price of the dress.

304 Okay, lets begin

305 $1600

306 <h3>Explanation</h3>

307 <ol><li>Calculating Discount:$ Discount = \frac{20}{100} × 2000 = 400$

308 </li>

309 <li>Calculating Selling price:$\text {Selling price} = 2000 - 400 = $1600$

310 </li>

311 </ol>The selling price of the dress is $1600.

312 Well explained 👍

313 <h3>Problem 4</h3>

314 A car travels at a speed of 80 km/h. How far will the car travel in 6 hours?

315 Okay, lets begin

316 480 km

317 <h3>Explanation</h3>

318 Using Distance formula:

319 $\text{ Distance = Speed × Time}\\ \space \\ \text{Distance = 80 × 6 = 480 km}$

320 The car will travel 480km in 6 hours.

321 Well explained 👍

322 <h3>Problem 5</h3>

323 A school has 100 boys and 80 girls. Calculate the ratio between boys and girls. Also, if the school plans to increase the number of boys and girls in the same ratio, how many boys will there be if the number of girls increases to 110?

324 Okay, lets begin

325 137.5 rounded to 138

326 So the ratio is 5:4 and the number of boys would be 138 boys.

327 <h3>Explanation</h3>

328 <ol><li>Ratio of boys to girls: ${100 \over {80}} = {5:4}$Ratio = 5:4

329 </li>

330 <li>Now we have to find the number of boys if girls increases to 110Let the number of boys be x.

331 Since the ratio is 5:4:

332 ⇒ $5:4 = x :110 $

333 </li>

334 <li>Doing cross multiplication:$ \begin{align*} 4x &= 5 × 110\\\\ 4x &= 550\\\\ x &= \frac{550}{4}\\\\ x &= 137.5 \end{align*} $

335 </li>

336 <li>Rounding 137.5 to the nearest whole number:= 138

337 </li>

338 </ol>Well explained 👍

339 <h2>FAQs on Commercial Math</h2>

340 <h3>1.What are the concepts that my child needs to know under commercial math?</h3>

341 Profit and loss, discounts, taxes, profit and losses are a few concepts that comes under commercial math, which chidlren have to learn.

342 <h3>2.How can my child calculate percentage?</h3>

343 To calculate percentage, teach these steps:

344 <ol><li>Dividing the given number by 100.</li>

345 <li>Multiplying the percentage with the resultant of the first step.</li>

346 </ol>Example: 20% of 200:

347 $\frac{200}{100} × 20 = 40$

348 So, $\text{20% of 200 is 40}$

349 <h3>3.How can my child easily understand commercial math?</h3>

350 Use real-life scenarios such as:

351 <ol><li>Calculate a discount during a shopping.</li>

352 <li>Calculate the final price of an item, including sales tax.</li>

353 <li>Discuss budgeting during family vacations.</li>

354 <li>Compare bank interest rates for savings.</li>

355 </ol><h3>4.What is the difference between math and commercial mathematics?</h3>

356 Math is all about the study of patterns, numbers, and shapes. Commercial mathematics is mainly used in businesses.

357 <h3>5.How can I help my child understand commercial math?</h3>

358 When shopping, give your child some money and ask them to buy necessities for themselves with that money. Guide them to help understand the prices, discounts, offers, limitations, taxes, etc. This will help them to understand basic terms of commercial math.

359 <h3>6.What are the formulas that my child needs to learn in commercial mathematics?</h3>

360 The important formulas that your child might need to learn are:

361 <ul><li>$\text{Simple interest }= \frac{P × R × T} {100}$ </li>

362 <li>$\text{Compound interest} = P × (1 + \frac {R}{100})^T - P$ </li>

363 <li>$\text{Profit = Selling price - Cost price}$ </li>

364 <li>$\text{Loss = Cost price - Selling price}$ </li>

365 <li>$\text{Discount = Marked price - Selling price}$ </li>

366 <li>$\text{Tax} ={ {\text{Rate × Value}} \over{100}}$ </li>

367 </ul><h3>7.Can my child master commercial math?</h3>

368 Yes, commercial math is practical mathematics. By connecting practical problems to real life situations, children can easily grasp it.

369 <h3>8.What are the future scope of using commercial mathematics for my child?</h3>

370 There are many jobs that children can pursue if they are interested in commercial maths. The following careers uses commercial maths:

371 <ul><li>Banking and Finance</li>

372 </ul><ul><li>Accounting and Auditing</li>

373 </ul><ul><li>Business Management</li>

374 </ul><ul><li>Insurance and Investments</li>

375 </ul><ul><li>Retail and Sales</li>

376 </ul><ul><li>Data Analysis and Economics </li>

377 </ul><h3>9.Is commercial mathematics hard for my child?</h3>

378 No, commercial math is considered an easier branch of mathematics, as it deals with real-life problems. This type of math is widely used in everyone's daily lives for various purposes and is generally easier for children compared to other branches of math.

379 <h3>10.What skill does my child develop by learning commercial math?</h3>

380 Commercial math will help your child to better understand their finances and to make informed and smart decision when managing money.

381 <h3>11.How to calculate discount percent?</h3>

382 The discount percent (or discount rate) tells you what percentage of the original price has been reduced. We can use the percentage formula as;

383 $\text{Discount percentage} = \frac{\text {Discount}} {\text{Marked Price}} \times 100$

384 <h2>Explore More Math Topics</h2>