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Rajesh and Manish have weights in the ratio of 3:4. They have N kilograms of mangoes. When Rajesh carries 60% of the mangoes, the ratio of his total weight to Manish’s weight becomes 9:10. If Manish carries 50% of the mangoes, what will be the ratio of Manish’s total weight to Rajesh’s weight?

Question

Rajesh and Manish have weights in the ratio of 3:4. They have N kilograms of mangoes. When Rajesh carries 60% of the mangoes, the ratio of his total weight to Manish’s weight becomes 9:10. If Manish carries 50% of the mangoes, what will be the ratio of Manish’s total weight to Rajesh’s weight?

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Solution

Let's denote the weights of Rajesh and Manish as 3x and 4x respectively.

Step 1: We know that Rajesh carries 60% of the mangoes, so his total weight becomes 3x + 0.6N.

Step 2: According to the problem, this total weight is in the ratio 9:10 with Manish's weight. So, we can write the equation: (3x + 0.6N) / 4x = 9/10

Step 3: Solving this equation for N, we get N = 20x.

Step 4: Now, if Manish carries 50% of the mangoes, his total weight becomes 4x + 0.5N = 4x + 0.5*20x = 14x.

Step 5: The ratio of Manish’s total weight to Rajesh’s weight is then 14x / 3x = 14/3.

So, the ratio of Manish’s total weight to Rajesh’s weight when Manish carries 50% of the mangoes is 14:3.

This problem has been solved

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