Question

The age of Hari and Harry are in the ratio 5:7, fours years from now the ratio of their ages will be 3:4, find their present ages.

Answer 1

haris age=5x
harrys age = 7x 
after 4 years their ages
hari=5x+4
harry=7x+4
their ratio=3:4
therefore,
5x+4/7x +4=3/4
on solving we get x=4
therefore haris age=20
harrys age=28.

Answer 2

Let the age of Hari be x
and Harry be y


$\frac{5}{7} = \frac{x}{y}$

7x = 5y

$\frac{7x}{5} = y$
......( i )


After 4 years

Hari :- x + 4
Harry :- y + 4

$\frac{x + 4}{y + 4} = \frac{3}{4}$

4x + 16 = 3y + 12

4x - 3y + 16 - 12 = 0

4x - 3y + 4 = 0


Putting value of y from ( i )

4x - 3 × 7x /5 + 4 = 0

$\frac{20x - 21x + 20}{5} = 0$


- x = - 20

x = 20


Putting value of x in ( i )

$\frac{7x}{5} = y$

$\frac{140}{5} = y$

28 = y

Hari age :- 20 years

Harry age :- 28 years