A shopkeeper buys rice at B per kg and sells… | GMAT Sprint

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PS · Problem Solving

705-805

percent

A shopkeeper buys rice at $B per kg and sells it for $S per kg. He cheats while selling rice and gives 20% less than the actual weight. If he makes a profit of 30% in a transaction, then find the ratio of B to S.

Correct answer marked below

8:13

10:13

25:26

Correct

26:25

13:8

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Explanation

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Official Explanation

Official

The shopkeeper buys 1kg of rice at $

B

.

He cheats by giving 20% less weight, so he sells only 0.8kg of rice at $

S

per kg.

Therefore, the selling price for 1kg of rice is $

\frac{S}{0.8} = \frac{5S}{4}

.

Profit on 1kg of rice = Selling price per kg - Cost price per kg =

\frac{5S}{4} - B = \frac{5S - 4B}{4}

.

Percentage Profit =

\frac{\frac{5S - 4B}{4}}{B} \times 100 = \frac{5S - 4B}{4B} \times 100

.…

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What this question tests

Your ability to apply GMAT math concepts to solve a multi-step problem quickly and accurately. At the 705-805 level, accuracy and speed both matter.

Overcomplicating the setup — most GMAT problems reward a direct, organized approach over brute calculation.