Question

Current age of Ritu and Rinki is in the ratio 3:4. Six years back, the ratio of their ages was 2:3. What is the present age of Ritu?

• A. \(12 \text{ years}\)
• B. \(18 \text{ years}\)
• C. \(20 \text{ years}\)
• D. \(22 \text{ years}\)

Hint:

When dealing with problems involving ratios of ages, always set the current ages in terms of a single variable using the given ratio, then work backwards or forwards as required by additional conditions.

Answer 1

The Correct Option is B

Step 1: Set up the equation based on the current age ratio.
Let \( R \) be Ritu's age and \( S \) be Rinki's age. According to the problem: \[ \frac{R}{S} = \frac{3}{4} \] Thus, we can express \( S \) in terms of \( R \): \[ S = \frac{4}{3}R \]

Step 2: Set up the equation for the ages six years ago.
Given the age ratio six years ago: \[ \frac{R - 6}{S - 6} = \frac{2}{3} \] Substituting \( S \) from the previous step: \[ \frac{R - 6}{\frac{4}{3}R - 6} = \frac{2}{3} \] Cross-multiplying to solve for \( R \): \[ 3(R - 6) = 2(\frac{4}{3}R - 6) \] Simplifying: \[ 9R - 18 = 8R - 12 \] \[ R = 18 \]