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Select the correct answerThe present ages of Amit and his father are in the ratio of 2 : 5 respectively. Four years hence the ratio of their ages will become 5 : 11 respectively. What was the father’s age 5 years ago?Options45 years40 years30 years35 years

Question

Select the correct answerThe present ages of Amit and his father are in the ratio of 2 : 5 respectively. Four years hence the ratio of their ages will become 5 : 11 respectively. What was the father’s age 5 years ago?Options45 years40 years30 years35 years

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Solution

Let's solve this step by step:

Step 1: Let's assume the present age of Amit is 2x and the present age of his father is 5x.

Step 2: According to the problem, four years from now, the ratio of Amit's age to his father's age will be 5:11. So, we can write this as (2x + 4) / (5x + 4) = 5/11.

Step 3: Cross-multiplying to solve for x, we get 11*(2x + 4) = 5*(5x + 4).

Step 4: Simplifying this, we get 22x + 44 = 25x + 20.

Step 5: Rearranging the terms, we get 25x - 22x = 44 - 20.

Step 6: Simplifying further, we get 3x = 24.

Step 7: Solving for x, we get x = 24/3 = 8.

Step 8: Substituting x = 8 in 5x (father's present age), we get 5*8 = 40 years.

Step 9: Therefore, the father's age 5 years ago was 40 - 5 = 35 years.

So, the correct answer is 35 years.

This problem has been solved

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