A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the…

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A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity (in kg.) sold at 18% profit is:

  1. A.

    560

  2. B.

    600

  3. C.

    400

  4. D.

    640

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Correct answer: B

Approach: use algebra to find the quantity sold at 18% profit.

  1. Let x be the kg sold at 18% profit. Then the rest is 1000 − x kg sold at 8% profit.

  2. Write the equation for the overall profit percentage: (18%×x + 8%×(1000 − x))/1000 = 14%.

  3. Multiply both sides by 1000: 18x + 8(1000 − x) = 14×1000.

  4. Simplify: 18x + 8000 − 8x = 14000 ⇒ 10x = 6000 ⇒ x = 600.

Therefore, 600 kg are sold at 18% profit.

Alternate (allegation) method:

  • Difference between 18% and mean 14% is 4; difference between mean 14% and 8% is 6.

  • Ratio of the portions = 4 : 6 = 2 : 3, so the portion at 18% is 3/5 of 1000 = 600 kg.

Answer: 600 kg.

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