Question

Two years ago, the ages of Rekha and Shruti were in the ratio 2:3. Three years hence, the ratio will become 3:4. How old will Shruti be after 8 years from now?

• A. 25 years
• B. 24 years
• C. 23 years
• D. 22 years

Hint:

Form equations using present ages

Answer 1

The Correct Option is A

Step 1: Define present ages.
Let Rekha's present age = \(R\), Shruti's present age = \(S\). Step 2: Form equation from two years ago.
Two years ago: \(\frac{R-2}{S-2} = \frac{2}{3}\).
Cross-multiply: \(3(R-2) = 2(S-2)\).
\(3R - 6 = 2S - 4\).
\(3R - 2S = 2\) …(1) Step 3: Form equation from three years hence.
Three years hence: \(\frac{R+3}{S+3} = \frac{3}{4}\).
\(4(R+3) = 3(S+3)\).
\(4R + 12 = 3S + 9\).
\(4R - 3S = -3\) …(2) Step 4: Solve equations (1) and (2).
Multiply (1) by 3: \(9R - 6S = 6\).
Multiply (2) by 2: \(8R - 6S = -6\).
Subtract: \((9R - 6S) - (8R - 6S) = 6 - (-6)\).
\(R = 12\). Step 5: Find \(S\) using (1).
\(3(12) - 2S = 2\).
\(36 - 2S = 2\).
\(-2S = -34\).
\(S = 17\). Step 6: Find Shruti's age after 8 years.
\(S + 8 = 17 + 8 = 25\) years.