Question

The ratio of present ages of r and s is 6:7. Before 12 years the ratio of their ages was 9:11. What is r's present age (in years)?

Answer 1

$\frac{r}{s} = \frac{6}{7} \\ 7r - 6s = 0.....1$
from 2nd condition
$\frac{r - 12}{s - 12} = \frac{9}{11} \\ 11r - 132 = 9s - 108 \\ 11r - 9s = - 108 + 132 \\ 11r - 9s = 24.....2$
multiply 1 with -3
$- 21r + 18x = 0....3$
multiply 2 with 2
$22r - 18x = 48.....4$
adding 3 and 4
$r = 48$
put r =48 in 1
$7 \times 48 - 6s = 0 \\ - 6s = - 336 \\ s = 56$
therefore the present age of r is 48 years and s is 56 years.
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