Question

The ratio of the ages of sameer and akhil two years ago was 2:3. Four years later from now the ratio of their ages will be 3:4. Find their present ages.

Answer 1

Let the present ages of sameer and akhil is x and y respectively. The ratio of the ages of sameer and akhil was 2:3 two years ago. Then,
x-2/y-2=2/3
or, 3x-6=2y-4
or, 3x-2y=-4+6
or, 3x-2y=2 --------------(1)
Four years later from now the ration of their ages will be 3:4. Then,
x+4/y+4=3/4
or, 4x+16=3y+12
or, 4x-3y=12-16
or, 4x-3y=-4 -------------(2)
Multiplying (1) with 4 and (2) with 3 we get,
12x-8y=8 -----------------(3)
12x-9y=-12 --------------(4)
Subtracting (4) from (3),
y=20
∴, 3x=2+2y
or, 3x=2+2×20
or, 3x=2+40
or, x=42/3
or, x=14
∴, Presents ages of sameer and akhil are 14 years and 20 years respectively.