Question

If the present ages of A and B are in the ratio 9 : 4 and seven years hence, the ratio of their ages will be 5 : 3, then find the their present ages.

Answer 1

Let the present ages of A and B be a and b

$\frac{a}{b}=\frac{9}{4}$

$a=\frac{9b}{4}$

After $7$ yrs ages of A and B will be $a+7$ & $b+7$

$\frac{a+7}{b+7}=\frac{5}{3}$

$3(a+7)=5(b+7)$

$3a+21=5b+35$

$3a=5b+14$

$3\left(\frac{9b}{4}\right)=5b+14$

$\frac{27b}{4}-5b=14$

$\frac{7b}{4}=14$

$b=2\times 4=8$

$a=\frac{9\times 8}{4}=9\times 2=18$

$\therefore$Present ages of A and B will be $18$ and $8$