A merchant buys 20 kg of wheat at Rs. 30 per kg and 40 kg of wheat at Rs. 25…

2026

A merchant buys 20 kg of wheat at Rs. 30 per kg and 40 kg of wheat at Rs. 25 per kg. He mixes them and sells one-third of the mixture at Rs. 26 per kg. At what price should the merchant sell the remaining mixture so that he earns a profit of 25% on the whole transaction?

  1. A.

    Rs 30

  2. B.

    Rs 36

  3. C.

    Rs 40

  4. D.

    Rs 37

Attempted by 11 students.

Show answer & explanation

Correct answer: D

Concept: When part of a mixture (bought at different cost rates) has already been sold, the price for the remaining portion is fixed by first finding the total cost price of the whole mixture, then the total selling price needed to earn the target profit percentage on that whole cost. The revenue already collected from the portion already sold is credited against this target, and the shortfall is spread over the remaining quantity.

Applying this to the given data:

  1. Cost of Batch 1 = 20 kg × Rs. 30/kg = Rs. 600.

  2. Cost of Batch 2 = 40 kg × Rs. 25/kg = Rs. 1000.

  3. Total cost price (CP) of the mixture = Rs. 600 + Rs. 1000 = Rs. 1600, over a total weight of 20 + 40 = 60 kg.

  4. Total selling price (SP) required for a 25% profit on the whole = CP × 1.25 = Rs. 1600 × 1.25 = Rs. 2000.

  5. Quantity already sold = one-third of 60 kg = 20 kg; revenue from this sale = 20 kg × Rs. 26/kg = Rs. 520.

  6. Revenue still required from the remaining 40 kg = Total SP needed − revenue already earned = Rs. 2000 − Rs. 520 = Rs. 1480.

  7. Required selling price for the remaining mixture = Rs. 1480 ÷ 40 kg = Rs. 37 per kg.

Cross-check: total revenue collected = Rs. 520 (from the first 20 kg) + Rs. 37 × 40 kg (Rs. 1480) = Rs. 2000. Profit earned = Rs. 2000 − Rs. 1600 = Rs. 400, which is exactly 25% of the Rs. 1600 cost price — confirming the target margin is met.

Therefore, the merchant should sell the remaining mixture at Rs. 37 per kg.

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