Question

The present age of Ishan is \(\frac{2}{5}\)th of the age of Subash. After 2 years, the age of Subash will be 2 times the age of Ishan. Two years back, the age of Subash was 4 times the age of Ishan. Find the present age of Ishan?

• A. 10
• B. 6
• C. 4
• D. Cannot be determined

Hint:

In problems involving age, set up equations based on the relationships given in the problem and solve step-by-step. Always check your results with the conditions provided.

Answer 1

The Correct Option is C

Let the present age of Ishan be \( x \). According to the problem, the present age of Subash will be \( \frac{5}{2} x \), since Ishan's age is \( \frac{2}{5} \)th of Subash's age. Step 1: Age after 2 years.
After 2 years, Ishan's age will be \( x + 2 \), and Subash's age will be \( \frac{5}{2}x + 2 \). According to the problem, after 2 years, Subash's age will be 2 times Ishan's age: \[ \frac{5}{2}x + 2 = 2(x + 2) \] Solve for \( x \): \[ \frac{5}{2}x + 2 = 2x + 4 \] \[ \frac{5}{2}x - 2x = 4 - 2 \] \[ \frac{1}{2}x = 2 \] \[ x = 4 \] Step 2: Verify using the condition 2 years ago.
Two years ago, the age of Ishan was \( x - 2 = 4 - 2 = 2 \), and the age of Subash was \( \frac{5}{2}x - 2 = \frac{5}{2} \times 4 - 2 = 10 - 2 = 8 \). According to the problem, two years ago, Subash's age was 4 times Ishan's age, and indeed \( 8 = 4 \times 2 \). Thus, the present age of Ishan is 4 years. Final Answer: \[ \boxed{4} \]