Multiple choice

A merchant is selling a type of grain (G1) at Rs. 50 per kilogram with no profit or loss. To boost his profit margins, he decides to mix the grain with a cheaper grain (G2) that costs Rs. 20 per kilogram. He plans to sell this new mixture at Rs. 45 per kilogram. Determine the ratio in which he should mix the two types of grain to make a profit of 20%.

  1. G1 : G2 = 8 : 7

  2. G1 : G2 = 7 : 8

  3. G1 : G2 = 7 : 5

  4. G1 : G2 = 5 : 7

  5. G1 : G2 = 5 : 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To make 20% profit on selling at 45, CP of mixture = 45 / 1.2 = 37.5. G1 cost = 50, G2 cost = 20. Alligation: (50 - 37.5) : (37.5 - 20) = 12.5 : 17.5 = 125 : 175 = 5 : 7.

AI explanation

The selling price of the mixture for a 20% profit is Rs. 45, so the cost price of the mixture is 45 divided by 1.2, which equals Rs. 37.5 per kilogram. Using the rule of alligation with the cost of G1 at Rs. 50, the mean price at Rs. 37.5, and the cost of G2 at Rs. 20 gives the ratio of their quantities. The ratio of G1 to G2 is calculated as (37.5 minus 20) to (50 minus 37.5), which is 17.5 to 12.5, simplifying to 7:5.

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