Question

The ratio of the ages of A and B is 4:5. After 6 years, the ratio becomes 5:6. What is the present age of A?

• A. 24 years
• B. 30 years
• C. 36 years
• D. 40 years

Hint:

• Represent present ages based on the given ratio: e.g., $4x$ and $5x$.
• Represent their ages after the specified number of years: $(4x+6)$ and $(5x+6)$.
• Set up an equation using the new ratio: $\frac{4x+6}{5x+6} = \frac{5}{6}$.
• Solve for $x$.
• Calculate the required present age (of A, which is $4x$).

Answer 1

The Correct Option is A

Let the present age of A be $4x$ years and the present age of B be $5x$ years. Then, the ratio of their present ages is: \[ \frac{4x}{5x} = \frac{4}{5} \] After 6 years:

• Age of A = $4x + 6$
• Age of B = $5x + 6$

Given that the ratio of their ages after 6 years is $5:6$: \[ \frac{4x + 6}{5x + 6} = \frac{5}{6} \] Cross-multiplying: \[ 6(4x + 6) = 5(5x + 6) \] \[ 24x + 36 = 25x + 30 \] \[ 36 - 30 = 25x - 24x \Rightarrow 6 = x \] Now compute their present ages: \[ \text{A's age} = 4x = 4 \times 6 = 24 \text{ years} \] \[ \text{B's age} = 5x = 5 \times 6 = 30 \text{ years} \] Check: After 6 years: \[ \text{A's age} = 24 + 6 = 30,\quad \text{B's age} = 30 + 6 = 36 \] \[ \text{Ratio} = \frac{30}{36} = \frac{5}{6} \quad \text{✓ Matches given condition} \] Final Answer: \[ \boxed{24 \text{ years}} \]