Question

The ages of two persons differ by 16 years. If 6 years ago, the elder one was three times as old as the younger one, then the present age of the elder one is:

• A. 14 years
• B. 30 years
• C. 20 years
• D. 15 years

Hint:

Use variables to express both current and past ages based on the condition, then form equations accordingly.

Answer 1

The Correct Option is B

Step 1: Let the present age of the younger be \( x \), then elder is \( x + 16 \). Step 2: Six years ago, \[ \text{Younger} = x - 6,\quad \text{Elder} = x + 16 - 6 = x + 10 \] Given: \[ x + 10 = 3(x - 6) \] Step 3: Solve the equation. \[ x + 10 = 3x - 18
28 = 2x \Rightarrow x = 14 \] So, elder = \( x + 16 = 14 + 16 = 30 \)