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
Here's your answer!!

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.

:. Age of sahil = 20 years.
Age of nikhil = 15 years.

HOPE IT HELPS!!

Answer 2

Present ages
Let the ages of Sahil and Nikhil be 4x and 3x. 

After 5 years
Age of Sahil = (4x+5)
Age of Nikhil = (3x+5)
Ratio of their ages = 5:4

Solve the equation
$\frac{4x+5}{3x+5} = \frac{5}{4}$
Cross multiply
$4(4x+5) = 5(3x+5)$
$16x+20 = 15x+25$
$16x-15x = 25-20$
$x = 5$

Present age of Sahil = 4x = 4 × 5 = 20
Present age of Nikhil = 3x = 3 × 5 = 15

Hope this may help you.