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10 years ago, the ratio of ages of A and B was in the ratio 7:10. 6 years hence, their ages will be in the ratio 5:6. What is the difference of their ages?1 point156124

Question

10 years ago, the ratio of ages of A and B was in the ratio 7:10. 6 years hence, their ages will be in the ratio 5:6. What is the difference of their ages?1 point156124

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Solution

Let's solve this step by step:

Step 1: Let's assume the ages of A and B 10 years ago were 7x and 10x respectively.

Step 2: This means that the present ages of A and B are 7x+10 and 10x+10 respectively.

Step 3: According to the problem, 6 years from now, the ratio of their ages will be 5:6. So, we can write the equation as (7x+10+6)/(10x+10+6) = 5/6.

Step 4: Simplifying the equation, we get (7x+16)/(10x+16) = 5/6.

Step 5: Cross-multiplying, we get 6*(7x+16) = 5*(10x+16).

Step 6: Simplifying, we get 42x + 96 = 50x + 80.

Step 7: Rearranging, we get 50x - 42x = 96 - 80.

Step 8: Simplifying, we get 8x = 16.

Step 9: Solving for x, we get x = 2.

Step 10: Substituting x = 2 in the equations for the present ages of A and B, we get A = 72+10 = 24 and B = 102+10 = 30.

Step 11: Therefore, the difference in their ages is 30 - 24 = 6 years.

This problem has been solved

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