Question

44. Eight years ago the ratio of the age of A to that of B was 5:7. After 16 years
the ratio of their ages will be 4:5. What is the difference between the present ages of
A and B ?
(a)
14 years
(b) 16 years
le)
18 years
(d) 20 years​

Answer 1

Let,

Eight year ago, ages of A and B are 5x years and 7x years respectively.

Then,

• Present age of A = 5x + 8

• Present age of B = 7x + 8

 $\displaystyle\sf{\frac{5x+8+16}{7x+8+16}=\frac{4}{5}$

$\displaystyle\sf{\implies 5(5x+24)=4(7x+24)$

$\displaystyle\sf{\implies 25x+120=28x+96$

$\displaystyle\sf{\implies 28x-25x=120-96$

$\displaystyle\sf{\implies 3x=24$

$\displaystyle\sf{\implies x=8$

$\displaystyle\sf{Present\:Age\:of\:A=(5\times 8)+8 =40+8=48$

$\displaystyle\sf{Present\:Age\:of\:B=(7\times 8)+8 =56+8=64$

$\displaystyle\sf{Age\:Difference=64-48=16$

$\boxed{\displaystyle\sf{Age\:Difference=(b)\:16\:Years}}$