A trader lost $ 20\%$ by selling a watch for $₹1,024 $. What percentage will he gain by selling it for $₹1,472

Question

A trader lost $ 20\%$ by selling a watch for $₹1,024 $. What percentage will he gain by selling it for $₹1,472 $?

Examoogle · Accepted Answer

The correct answer is Option A: 15%. Use ratio of selling prices: $\frac{SP_2}{SP_1} = \frac{1,472}{1,024} = 1.4375$. Since $SP_1$ represents 80% of Cost Price, $SP_2$ represents $80 	imes 1.4375 = 115\%$. Gain = $115\% - 100\% = 15\%$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use ratio of selling prices: $\frac{SP_2}{SP_1} = \frac{1,472}{1,024} = 1.4375$. Since $SP_1$ represents 80% of Cost Price, $SP_2$ represents $80 	imes 1.4375 = 115\%$. Gain = $115\% - 100\% = 15\%$.

Formula Used: $$CP = \frac{SP}{1 - 	ext{Loss}\%}, \quad 	ext{Gain}\% = \frac{SP - CP}{CP} 	imes 100$$

Given: Loss percentage = 20%, Selling Price 1 = ₹1,024, Selling Price 2 = ₹1,472.

Steps: Calculate Cost Price (CP): Since selling at ₹1,024 results in a 20% loss, the SP is 80% of the CP.. Determine Profit for new SP: Calculate the difference between the new selling price and the cost price.. Calculate Gain Percentage: Divide profit by CP and multiply by 100 to get the gain percentage.

Answer: A is correct because the calculated cost price is ₹1,280 and selling it for ₹1,472 results in a profit of ₹192, which is 15% of the cost price.

Exam Tip: This ratio-based approach is similar to finding effective percentage changes in compound interest or successive discounts.

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