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The 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?Options35 years45 years40 years30 years

Question

The 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?Options35 years45 years40 years30 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 hence, the ratio of their ages will be 5 : 11. So, we can write it as (2x + 4) / (5x + 4) = 5 / 11.

Step 3: Cross-multiplying the above equation, we get 22x + 88 = 25x + 20.

Step 4: Simplifying the equation, we get 3x = 68.

Step 5: Solving for x, we get x = 68 / 3 = 22.67 (approximately).

Step 6: Substituting x = 22.67 in 5x (father's present age), we get 5 * 22.67 = 113.33 (approximately).

Step 7: The father's age 5 years ago would be 113.33 - 5 = 108.33. But since age is always a whole number, we round it off to the nearest whole number, which is 108.

However, none of the options match this result. There might be a mistake in the problem or the options provided.

This problem has been solved

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