Arithmetic

Profit & Loss

Medium

By selling 32 apples for Rs 30, a man loses 25%. How many apples should be sold for Rs 24, to gain 20% in the transaction?

✅ Correct Option: 4

32 apples are sold for Rs 30 with a 25% loss.

When there's a 25% loss, the selling price is 75% of the cost price (100% - 25% = 75%).

Selling Price = 0.75 × Cost Price

$30 = 0.75 \times \text{CP}$

$\text{CP} = 30 \div 0.75$

$\text{CP} = 40$

The cost price of 32 apples is Rs 40.

Cost of 1 apple:

$\text{Cost per apple} = 40 \div 32$

$\text{Cost per apple} = 1.25$

Let $x$ be the number of apples to be sold for Rs 24 with a 20% profit.

Cost Price of $x$ apples $= 1.25x$

For 20% profit, the selling price should be 120% of the cost price (100% + 20% = 120%).

$\text{Selling Price} = 1.20 \times \text{Cost Price}$

$24 = 1.20 \times (1.25x)$

$24 = 1.5x$

$x = 24 \div 1.5$

$x = 16$

Therefore, 16 apples should be sold for Rs 24 to gain 20% in the transaction.

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By selling 32 apples for Rs 30, a man loses 25%. How many apples should be sold for Rs 24, to gain 20% in the transaction?

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