Question

Before 7 years the ratio of ages a and b was 3:4 after 9years the ratio of their ages will be 7:8 what is the current age of b

Answer 1

7 years is the correct answer

Answer 2

Let the present age of A be = x years
and present age of B be = y years
According to the question
7 years ago
$\frac{x - 7}{y - 7} = \frac{3}{4} \\ 4(x - 7) = 3(y - 7) \\ 4x - 28 = 3y - 21 \\ 4x - 3y = 7 \: \: \: \: \: \: \: \: \: \: \: ......(1) \\ after \: 9 \: years \\ \frac{x + 9}{y + 9} = \frac{7}{8} \\ 8(x + 9) = 7(y + 9) \\ 8x + 72 = 7y + 63 \\ 8x - 7y = - 9 \: \: \: \: \: ......(2) \\ multiply \: equation \: (1) \: by \: 2 \: we \: get\\ 8x - 6y = 14 \: \: \: \: \: ......(3) \\ 8x - 7y = - 9 \: \: \: \: \: ....(2) \\ subtract \: equation \: (2) \: from \: equation(3) \: we \: get \\ y = 23 \\ present \: age \: of \: B = 23 \: years \\ put \: the \: value \: of \: y \: in \: equation \: (1) \: \\ 4x - 3(23) = 7 \\ 4x - 69 = 7 \\ 4x = 76 \\ x = 19 \\ present \: age \: of \: A \: = 19 \: years$