What will be the age of R after two years?

Given the following statements:

I. The average age of A and N is 24 years, and the ratio of the age of R to A is 2 : 3.

II. N is 4 years older than S, and the ratio of the age of S to R is 1 : 2.

Question

What will be the age of R after two years?

Given the following statements:

I. The average age of A and N is 24 years, and the ratio of the age of R to A is 2 : 3.

II. N is 4 years older than S, and the ratio of the age of S to R is 1 : 2.

Accepted Answer

**Solution:**

1. From statement I:
   - Average age of A and N = 24 years
   - So, total age of A and N = 24 × 2 = 48 years
   - Ratio of age of R to A = 2 : 3
   - Let age of R = 2k and age of A = 3k
   - But we do not know N's age or R's exact age yet, so statement I alone is insufficient.

2. From statement II:
   - N is 4 years older than S
   - Ratio of age of S to R = 1 : 2
   - Let age of S = x years
   - Then age of R = 2x years
   - Age of N = x + 4 years
   - We do not know A's age here, so statement II alone is insufficient.

3. Combining both statements:
   - From statement I, total age of A and N = 48 years
   - From statement II, N = x + 4
   - From statement I, A = 3k and R = 2k
   - From statement II, R = 2x
   - Since R = 2k and R = 2x, we get k = x
   - So, A = 3x and N = x + 4
   - Total age of A and N = 3x + (x + 4) = 4x + 4 = 48
   - 4x = 44 ⇒ x = 11

4. Therefore,
   - Age of R = 2x = 2 × 11 = 22 years
   - Age of R after 2 years = 22 + 2 = 24 years

**Answer:** Both statements I and II together are sufficient to find the age of R after two years.

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