WBBSE Class 9 Maths Arithmetic Chapter 2 Profit And Loss Multiple Choice Questions
Example 1. The ratio of cost price and selling price is 10: 11, the profit percentage is
- 9
- 11
- 10\(\frac{1}{9}\)
- 10
Solution: The ratio of cost price and selling price is 10: 11
⇒ Let cost price is ₹10x and selling price is ₹11x [x is common multiple and x > 0]
⇒ Profit = ₹(11x – 10x) = ₹x
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∴ Profit percentage = \(\frac{\text { Total profit }}{\text { Cost price }} \times 100\)
= \(\frac{x}{10 x} \times 100\) = 10
∴ The correct answer is 4. 10
The profit percentage is 10
Example 2. Buying a book at 40 and selling it at 60, the profit percentage will be
- 50
- 33\(\frac{1}{3}\)
- 20
- 30
Solution: C. P. = ₹40, S. P. = ₹60
Profit = ₹(60-40) = ₹20
Profit percentage = \(\frac{20}{40}\) x 100 = 50
∴ The correct answer is 1. 50
The profit percentage will be 50
Example 3. A shirt is sold at 360 and there is a loss of 10%. The cost price of the shirt is
- ₹380
- ₹400
- ₹420
- ₹450
Solution: Let the cost price of the shirt is ₹x
S.P. = ₹360
⇒ Loss percentage = \(₹ \frac{x-360}{x} \times 100\)
⇒ According to condition, \(\frac{x-360}{x} \times 100=10\)
⇒ \(\frac{x-360}{x}=\frac{10}{100}=\frac{1}{10}\)
⇒10x – 3600 = x
⇒ 9x = 3600
⇒ x = \(\frac{3600}{9}\) = 400
∴ The cost price is 400
∴ The correct answer is 2. ₹400
The cost price of the shirt is ₹400
Example 4. After 20% discount, the selling price of a geometry box becomes ₹48. The marked price of the geometry box is
- 60
- 75
- 48
- 50
Solution: Let the market price of the geometry box is ₹x [x > 0]
⇒ The selling price of the box after 20% discount is \(₹\left(x-x \times \frac{20}{100}\right)=₹ \frac{4 x}{5}\)
⇒ As per question, \(\frac{4 x}{5}\) = 48
⇒ x = \(\frac{5 \times 48}{4}\)
⇒ x = 60
∴ The marked price is 60
∴ The correct answer is 60
The marked price of the geometry box is 60
Example 5. A retailer buys medicine at 20% discount on marked price and sells to buyers at marked price. The retailer makes a profit percentage.
- 20
- 25
- 10
- 30
Solution: Let the marked price of medicine is ₹x [x > 0]
⇒ A retailer buys medicine at 20% discount on marked price
⇒ Cost price of medicine is \(₹\left(x-x \times \frac{20}{100}\right)=₹ \frac{4 x}{5}\)
⇒ Selling price of medicine is ₹x
∴ Profit = \(₹\left(x-\frac{4 x}{5}\right)=₹ \frac{x}{5}\)
∴ Profit percentage = \(\frac{\frac{x}{5}}{\frac{4 x}{5}} \times 100\)
= \(\frac{x}{5} \times \frac{5}{4 x} \times 100=25\)
∴ The correct answer is 2. 25
The retailer makes a profit percentage 25
Example 6. If a person sells an article for 300, gaining \(\frac{1}{4}\)th of its cost price, then gain percentage
- 15
- 20
- 25
- 30
Solution: Let the C.P. of the article be ₹x [x > 0]
⇒ gain = ₹\(\frac{x}{4}\)
⇒ S. P. = \(₹\left(x+\frac{x}{4}\right)=₹ \frac{5 x}{4}\)
\(\frac{5 x}{4}=300\)⇒ \(x=\frac{300 \times 4}{5}=240\)
∴ C.P. = ₹240
∴ gain = ₹(300 – 240) = ₹60
⇒ gain percentage = \(\frac{6}{240}\) x 100 = 25
∴ The correct answer is 3. 25
The gain percentage 25
Example 7. If a% loss is on cost price then loss percentage on selling price is
- \(₹ \frac{100 a}{100-a}\)
- \(₹ \frac{100-a}{100 a}\)
- \(₹ \frac{100 a}{100+a}\)
- \(₹ \frac{100+a}{100 a}\)
Solution: If cost price is ₹100 then selling price is ₹(100 – a)
⇒ If selling price is ₹(100 a) then loss is ₹a
⇒ If selling price is ₹1 then loss is \(₹ \frac{a}{100-a}\)
⇒ If selling price is ₹100 then loss is \(₹ \frac{100 a}{100-a}\)
∴ Loss is \(₹ \frac{100 a}{100-a}\)
∴ So the correct answer is 1. \(₹ \frac{100 a}{100-a}\)
Loss percentage on selling price is \(₹ \frac{100 a}{100-a}\)
Example 8. If the ratio of cost price and selling price x: y [0 < x < y], the profit percentage is
- \(\frac{y-x}{100 x}\)
- \(\frac{100(y-x)}{x}\)
- \(\frac{100(x-y)}{y}\)
- \(\frac{100(x+y)}{y}\)
Solution: Let cost price is ₹ax and selling price is ₹ay.
Profit = ₹(ay – ax) = ₹ a (y – x)
∴ Profit percentage = \(\frac{a(y-x)}{a x} \times 100=\frac{100(y-x)}{x}\)
∴ So the correct answer is 2. \(\frac{100(y-x)}{x}\)
The profit percentage is \(\frac{100(y-x)}{x}\)