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Select the correct answerThe ratio of the ages of Ram and Rahim 10 years ago was 1 : 3. The ratio of their ages 5 Years hence will be 2 : 3. Then, the ratio of their present ages is?Options1 : 23 : 42 : 53 : 5

Question

Select the correct answerThe ratio of the ages of Ram and Rahim 10 years ago was 1 : 3. The ratio of their ages 5 Years hence will be 2 : 3. Then, the ratio of their present ages is?Options1 : 23 : 42 : 53 : 5

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Solution

To solve this problem, we need to use the information given about the ratios of Ram and Rahim's ages at different points in time.

  1. 10 years ago, the ratio of Ram's age to Rahim's age was 1:3. Let's assume that 10 years ago, Ram was x years old and Rahim was 3x years old.

  2. The problem also tells us that in 5 years, the ratio of their ages will be 2:3. This means that in 5 years, Ram will be 2y years old and Rahim will be 3y years old.

  3. However, we know that "in 5 years" for Ram is actually x + 15 years (since we started when he was x years old and 10 years have already passed), and for Rahim it's 3x + 15 years.

  4. Setting these equal to the 2y and 3y we found earlier, we get the following two equations:

    x + 15 = 2y 3x + 15 = 3y

  5. Solving these equations, we find that x = 5, y = 10.

  6. Therefore, the present ages of Ram and Rahim are x + 10 = 15 and 3x + 10 = 25 respectively.

  7. So, the ratio of their present ages is 15:25, which simplifies to 3:5.

Therefore, the correct answer is 3:5.

This problem has been solved

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