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Question

The ratio of the present age of X to that of Y is 4 : 5. k (less than 10) years ago, this ratio was 1 : 2. How many values of k are possible if the ages are expressed in complete years ?

This question was previously asked in
CDS 1 2026 Maths Question Paper (12-Apr-2026)
The correct answer is

3

To solve this problem, we start by understanding the information given:

  • The current age ratio of X to Y is 4:5.
  • k years ago, this ratio was 1:2. Here, k is less than 10.

Let's denote the present age of X as 4x and the present age of Y as 5x, based on the given ratio 4:5.

Step 1: Setting up the equation for k years ago:

The ages k years ago would be:

  • Age of X: \(4x - k\)
  • Age of Y: \(5x - k\)

According to the problem, k years ago, the ratio was 1:2, hence:

\(\frac{4x - k}{5x - k} = \frac{1}{2}\)

Cross-multiplying gives us:

\(2(4x - k) = 1(5x - k)\)

This simplifies to:

\(8x - 2k = 5x - k\)

Rearranging terms, we get:

\(3x = k\)

Since k must be less than 10, feasible integer values for x such that 3x is an integer and less than 10 are:

Step 2: Calculating feasible values for k

  • If \(x = 1\), \(k = 3 \times 1 = 3\)
  • If \(x = 2\), \(k = 3 \times 2 = 6\)
  • If \(x = 3\), \(k = 3 \times 3 = 9\)

These are all the possible values for k, as any value of x greater than 3 would result in k being 10 or more, which is not permissible by the problem statement.

Therefore, there are 3 possible values for k: 3, 6, and 9.

Conclusion: The correct answer is that there are 3 possible values of k.

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Important Questions from Age

  1. In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth?

  2. A watch loses 2 minutes in every 24 while another watch gains 2 minutes, in 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24- hour clock is

  3. The sum of the ages of 5 members comprising a family, 3 years ago was 80 years. The average age of the family today is the same as it was 3 years ago, because of an addition of a baby during the intervening period. How old is the baby ?

  4. 5 years ago, my sister's age was 5 times my age. Now it is 3 times only. What is my sister's present age (in years)?

  5. The sum of ages of a father and his son is 45 years. Five years ago, the product of their ages (in yrs.) was 124. The present age of father is :

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