Multiple choice

Mukesh is a retailer. He does not make any profit if he sells a mixture of 10 kg of low quality pulses and 15 kg of high quality pulses at a price 40% more than that of low quality pulses. Find the ratio of cost price of low quality pulses to that of high quality pulses per kg?

  1. 2 : 5

  2. 3 : 5

  3. 4 : 5

  4. 5 : 8

  5. 7 : 8
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B Correct answer
Explanation

Let CP of low quality be L and high quality be H. Total cost = 10L + 15H. Selling price = 1.4 * (10L + 15H) / 25. Since there is no profit, SP = CP per unit. 1.4 * (10L + 15H) / 25 = (10L + 15H) / 25 is not right. The mixture is sold at 1.4 * L. Total SP = 25 * 1.4 * L = 35L. Total CP = 10L + 15H. 35L = 10L + 15H => 25L = 15H => L/H = 15/25 = 3/5.

AI explanation

By applying the rule of alligation on the high quality and low quality pulses, the ratio of their cost prices equals the ratio of the quantities of the other type. The ratio of the cost price of low quality pulses to high quality pulses is therefore equal to the ratio of the quantity of high quality pulses to low quality pulses, which is 15 kg : 10 kg. Simplifying this ratio gives the final result of 3 : 5.

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