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Select the correct answerThe present ages of A and B are in the ratio 3 : 4. Ten years ago, this ratio was 4 : 7. The present ages of A and B are respectively?Options18 years, 24 years24 years, 32 years27 years, 36 years21 years, 28 years

Question

Select the correct answerThe present ages of A and B are in the ratio 3 : 4. Ten years ago, this ratio was 4 : 7. The present ages of A and B are respectively?Options18 years, 24 years24 years, 32 years27 years, 36 years21 years, 28 years

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Solution

Let's solve this step by step:

Step 1: Let's assume the present ages of A and B are 3x and 4x respectively.

Step 2: According to the problem, ten years ago, the ratio of their ages was 4 : 7. So, (3x - 10) / (4x - 10) = 4/7.

Step 3: Cross multiply to solve for x. We get 7*(3x - 10) = 4*(4x - 10).

Step 4: Simplify to get 21x - 70 = 16x - 40.

Step 5: Rearrange to find the value of x. We get 21x - 16x = 70 + 40, which simplifies to 5x = 110.

Step 6: Solve for x. We get x = 110 / 5 = 22.

Step 7: Substitute x = 22 into the expressions for the ages of A and B. We get A = 3x = 322 = 66 and B = 4x = 422 = 88.

So, the present ages of A and B are 66 and 88 years respectively. However, these options are not available in the given choices. There seems to be a mistake in the problem or the options provided.

This problem has been solved

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