Multiple choice

A trader has 50 kg of rice, a part of which he sells at 10 percent profit and the rest at 5 percent loss. He gains 7 percent on the whole. What is the quantity sold at 10 percent gain and 5 percent loss?

  1. 30 kg and 10 kg

  2. 40 kg and 15 kg

  3. 35 kg and 40 kg

  4. 40 kg and 10 kg

  5. none of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the allegation method, the ratio of quantities sold at 10% profit and 5% loss is (7 - (-5)) : (10 - 7) = 12 : 3 = 4 : 1. For a total of 50 kg, the quantities are 40 kg and 10 kg.

AI explanation

Apply the alligation method to find the ratio of the quantities sold at a 10% profit and a 5% loss against the overall gain of 7%. The ratio of the profit/loss values is 10% to -5%, which when compared to the mean of 7% gives a ratio of (7 - (-5)) : (10 - 7). This simplifies to 12 : 3, or 4 : 1. Out of the total 50 kg, the quantities are (4/5) * 50 = 40 kg sold at a gain and (1/5) * 50 = 10 kg sold at a loss.

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