Question

Present ages of Sita and Geeta are in the ratio 4 : 5. Eight years from now the ratio of their ages will be 5 : 6. Find their present ages. [4 MARKS]

Answer 1

Concept: 2 Marks
Application: 2 Marks

Let the present ages of Sita and Geeta be 4x years and 5x years respectively.

After eight years. Sita’s age
$=(4x+8)years$;

After eight years, Geeta’s age
$=(5x+8)years$.

Therefore, the ratio of their ages after eight years
$=\frac{4x+8}{5x+8}=\frac{5}{6}$

Cross-multiplication gives
$6(4x+8)=5(5x+8)$

$24x+48=25x+40$

$24x+48–40=25x$

$24x+8=25x$

$8=25x–24x$

$8=x$

Therefore, Sita’s present age
$=4x=4\times 8=32years$

Geeta’s present age
$=5x=5\times 8=40years$