correct answer is: c) 48 & 18

Explanation

The A and B age ratio is 8 : 3.
Let, A’s present age ‘8x’
B’s present age ‘3x’
\therefore Six years hence A’s age is =\ 8x+6
And, Six years hence B’s age is =\ 3x+6
According to the question,
\left(8x+6\right)\ ∶\ \left(3x+6\right)\ =\ 9\ ∶\ 4
\rightarrow\ \frac{8x+6}{3x+6}\ =\ \frac{9}{4}
\rightarrow\ 4\left(8x+6\right)\ =\ 9\left(3x+6\right)
\rightarrow\ 32x\ +\ 24\ =\ 27x\ +\ 54
\rightarrow\ 32x\ -\ 27x\ =\ 54\ -\ 24
\rightarrow\ 5x\ =\ 30
\rightarrow\ x\ =\ \frac{30}{5}
\rightarrow\ x\ =\ 6
\therefore A’s present age ‘8x’ or \left(8\times6\right)
\rightarrow\ 48
and, B’s present age ‘3x’ or \left(3\times6\right)
\rightarrow\ 18
Ans: A’s present age is 48,
and B’s present age is 18.