Question

Six years ago, the ratio of the ages of Ram and Ravi was 6 : 5. Four years hence, the ratio of their ages will be 11:10. What is Ravi's age at present?

• A. 18 years
• B. 20 years
• C. 15 years
• D. 16 years

Hint:

To solve age ratio problems with conditions at two time points, form and solve simultaneous equations using algebra.

Answer 1

The Correct Option is D

Step 1: Let present ages of Ram and Ravi be \( x \) and \( y \). From 6 years ago: \[ \frac{x - 6}{y - 6} = \frac{6}{5} \quad \cdots (1) \] From 4 years hence: \[ \frac{x + 4}{y + 4} = \frac{11}{10} \quad \cdots (2) \] Step 2: Cross-multiplying both equations. From (1): \[ 5(x - 6) = 6(y - 6) \Rightarrow 5x - 30 = 6y - 36 \Rightarrow 5x - 6y = -6 \quad \cdots (3) \] From (2): \[ 10(x + 4) = 11(y + 4) \Rightarrow 10x + 40 = 11y + 44 \Rightarrow 10x - 11y = 4 \quad \cdots (4) \] Step 3: Solve equations (3) and (4). Multiply (3) by 2: \[ 10x - 12y = -12 \quad \cdots (5) \] Now subtract (4) from (5): \[ (10x - 12y) - (10x - 11y) = -12 - 4 \Rightarrow -y = -16 \Rightarrow y = 16 \] So Ravi's current age is \( \boxed{16} \)