Question

The ratio of the ages of A and B is 5:3. After 6 years, their ages will be in the ratio 6:4. What is the current age of A?

• A. 15 years
• B. 18 years
• C. 30 years
• D. 25 years

Hint:

Solve age-related problems by defining variables based on ratios and setting up equations for future conditions.

Answer 1

The Correct Option is C

Step 1: Define variables 
Let current age of A = $5x$ years, B = $3x$ years. 
Step 2: Set up equation after 6 years 
After 6 years, A’s age = $5x + 6$, B’s age = $3x + 6$. 
Given ratio: $\frac{5x + 6}{3x + 6} = \frac{6}{4}$. 
Step 3: Solve the equation 
Cross-multiply: $4(5x + 6) = 6(3x + 6)$. 
$\Rightarrow 20x + 24 = 18x + 36$. 
$\Rightarrow 20x - 18x = 36 - 24$. 
$\Rightarrow 2x = 12$. 
$\Rightarrow x = 6$. 
Step 4: Find A’s age 
Current age of A = $5x = 5 \times 6 = 30$ years.