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A bought an item for ₹384 and sold it for ₹576. B bought another item for ₹1,254 and sold it for ₹1,672. What is the ratio of the gain percentage of A to the gain percentage of B?
23
43
35
25
23
Calculate individual gains relative to cost price as fractions. A's gain ratio = (576-384)/384 = 192/384 = 1/2. B's gain ratio = (1672-1254)/1254 = 418/1254 = 1/3. Ratio of gains = (1/2) / (1/3) = 3/2.
A bought for ₹384 and sold for ₹576. B bought for ₹1,254 and sold for ₹1,672.
Gain percentage=(Cost PriceSelling Price−Cost Price)×100
Calculate individual gains relative to cost price as fractions. A's gain ratio = (576-384)/384 = 192/384 = 1/2. B's gain ratio = (1672-1254)/1254 = 418/1254 = 1/3. Ratio of gains = (1/2) / (1/3) = 3/2.
Many students mistake gain amount for gain percentage; the gain percentage must be calculated relative to the specific cost price of each person.
Calculate gain percentage for A
A's Cost Price (CP) = 384, Selling Price (SP) = 576. Gain = 576 - 384 = 192. Gain percentage = (192 / 384) * 100 = 0.5 * 100 = 50%.
GainA=384192=50%
Calculate gain percentage for B
B's Cost Price (CP) = 1254, Selling Price (SP) = 1672. Gain = 1672 - 1254 = 418. Gain percentage = (418 / 1254) * 100. Since 418 * 3 = 1254, this simplifies to (1/3) * 100 = 33.33%.
GainB=1254418=31≈33.33%
Find ratio of gain percentages
The ratio of A's gain % to B's gain % is 50% / (100/3)% = 50 * (3 / 100) = 150 / 100 = 3/2.
100/350=100150=23
A is correct because the ratio of the gain percentages of A and B is calculated as 50% to 33.33%, which simplifies to 3/2.
This type of ratio comparison is common in Data Interpretation questions where you need to quickly approximate fractions like 418/1254 as 1/3.
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