Question

find the answer the ages of sahil and nikhil are in the form of ratio 4:3.five years hence the ratio of their ages will be 5:4 . find the present age

Answer 1

Hey there!

Let the present age of Sahil be x
and the present age of Nikhil be y

∴ x/y = 4/3
⇒ 3x = 4y
⇒ 3x - 4y = 0 -----(1)

Also,
x+5/y+5 = 5/4
⇒ 4(x+ 5) = 5(y + 5)
⇒ 4x + 20 = 5y + 25
⇒ 4x - 5y = 5 -----(2)

Multiplying (1) with 5, we get
15x - 20y = 0

Multiplying (2) with 4, we get 
16x - 20y = 20

Solving (1) and (2)

15x - 20y = 0
16x - 20y = 20. (-)
⇒ x = 20

∴ 3x = 4y
⇒ 3 × 20/4 = y
⇒ 15 = y.

∴ Present Age of Sahil = 20 years.
Present Age of Nikhil = 15 years.

Cheers!

Answer 2

4x+5+3x+5=5x+4x
7x+10=9x
9x-7x=10
2x=10
x=10/2
x=5
Age of sahil =4*5=20
Age of nikhil =3*5=15