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Select the correct answerEighteen years ago, the ratio of A’s age to B’s age was 8 : 13. Their present ratios are 5 : 7. What is the present age of A ?Options60 years50 years40 years70 years

Question

Select the correct answerEighteen years ago, the ratio of A’s age to B’s age was 8 : 13. Their present ratios are 5 : 7. What is the present age of A ?Options60 years50 years40 years70 years

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Solution

To solve this problem, we need to use the concept of ratios and simple algebra. Here are the steps:

Step 1: Let's denote the present ages of A and B as A and B respectively. According to the problem, 18 years ago, the ratio of A's age to B's age was 8:13. So, we can write this as:

(A - 18) / (B - 18) = 8 / 13

Step 2: The problem also states that their present ages are in the ratio 5:7. So, we can write this as:

A / B = 5 / 7

Step 3: Now we have a system of two equations. We can solve this system by substitution or elimination method. Let's multiply the second equation by B to isolate A:

A = 5B / 7

Step 4: Substitute A from the second equation into the first equation:

(5B / 7 - 18) / (B - 18) = 8 / 13

Step 5: Solve this equation for B. After solving, you will get B = 70.

Step 6: Substitute B = 70 into the equation A = 5B / 7 to find A. After substituting, you will get A = 50.

So, the present age of A is 50 years. Therefore, the correct answer is 50 years.

This problem has been solved

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