Question

The present ages of A and B are in the ratio 17:9 . Ifthe ratio of the ages, 9 years ago was 7 :3 ,then find their present ages

Answer 1

let the present age of A be x and B be y.
According to first condition
$\frac{x}{y} = \frac{17}{9} \\ 9x - 17y = 0.......1$
According to second condition
$\frac{x - 9}{y - 9} = \frac{7}{3} \\ 3(x - 9) = 7(y - 9) \\ 3x - 27 = 7y - 63 \\ 3x - 7y = - 63 + 27 \\ 3x - 7y = - 36......2$
multiply 2 with -3
we get
$- 9x + 21y = 108....3$
Adding 1 and 3
we get
$4y = 108 \\ y = \frac{108}{4} \\ y = 27$

put y=27 in 1
$9x - 17 \times 27 = 0 \\ 9x - 459 = 0 \\ 9x = 459 \\ x = \frac{459}{9} \\ x = 51$
Therefore, age of A is 51 and B is 27.
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