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A shopkeeper bought some wheat. 25% of wheat was sold at 25% loss and 20% of the wheat is sold at 20% loss. At what percent gain (nearest to integers) should he sell the rest wheat to gain 30% on the whole transaction?

A shopkeeper bought some wheat. 25% of wheat was sold at 25% loss and 20% of the wheat is sold at 20% loss. At what percent gain (nearest to integers) should he sell the rest wheat to gain 30% on the whole transaction? Correct Answer 73%

Let the total quantity of the wheat be 100 kg and CP of the 100 kg wheat is Rs. 100.

25% of the wheat = 100 kg × 25/100 = 25 kg

20% of the wheat = 100 kg × 20/100 = 20 kg

Remaining wheat = 100 kg – 25 kg – 20 kg = 55 kg

Let 55 kg wheat sold at x% profit.

According to the question

25 × + 20 × + 55 × = 100 × 130/100

18.75 + 16 + 55 = 130

55 = 130 – 18.75 – 16 = 95.25

(100 + x)/100 = 95.25/55

(100 + x) = × 100 = 173

⇒ x = 173 – 100 = 73%

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