Question

The ratio of the present ages of X and Y is 4 : 9. After 8 years, the ratio will be 6 : 11. The present age of Y is

• A. 45 years
• B. 54 years
• C. 38 years
• D. 36 years

Hint:

Notice the change in ratio units over 8 years:
For X: \(4 \to 6\) (increase of \(2\) units).
For Y: \(9 \to 11\) (increase of \(2\) units).
Since the increase in units is equal for both (\(2\) units), we can directly equate:
\(2 \text{ units} = 8 \text{ years} \implies 1 \text{ unit} = 4 \text{ years}\).
Present age of Y = \(9 \text{ units} \times 4 = 36 \text{ years}\). This takes only seconds to solve!

Answer 1

The Correct Option is D

Step 1: Express present ages using the ratio.
Present ratio X:Y = 4:9. Let X = 4k and Y = 9k.
Step 2: Form and solve the equation from the future ratio.
After 8 years: (4k + 8)/(9k + 8) = 6/11. Cross-multiplying: 44k + 88 = 54k + 48, giving 10k = 40, so k = 4.
Step 3: Find Y's present age.
Y = 9 x 4 = 36 years. Verify: after 8 years X = 24, Y = 44, ratio = 24:44 = 6:11.
\[ \boxed{36} \]