Question

Two years hence, the respective ratio between A's age at that time and B's age at that time will be 6:5. A's age 13 years ago was half of B's present age. What is A's present age?

• A. 16 years
• B. 40 years
• C. 28 years
• D. 22 years
• E. 34 years

Answer 1

Answer: (D)

22 years

Let the A's present age be x years
and B's present age be y years.
Then, according to the question,
$\frac{x+2}{y+2}=\frac{6}{5}\Rightarrow 5x+10=6y+12\Rightarrow 5x-6y=12-10\Rightarrow 5x-6y=2\Rightarrow 5x-2=6y\Rightarrow \frac{5x-2}{6}=y\Rightarrow y=\frac{5x-2}{6}\left(i\right)x-13=\frac{1}{2}y\Rightarrow x=\frac{1}{2}y+13\Rightarrow 2x=y+26\Rightarrow 2x=\frac{5x-2}{6}+26[\because y=\frac{5x-2}{6}]\Rightarrow 12x=5x-2+156\Rightarrow 12x-5x=154\Rightarrow 7x=154\Rightarrow x=22$
Thus, present age of A = 22 years