Question

Four years ago, the ages of Raju and Rahul were in the ratio 3:8 . Five years hence, their ages will be in
the ratio3:5. Find their present ages.

Answer 1

Given :

• Four years ago, the ages of Raju and Rahul were in the ratio 3 : 8

• Five years hence, their ages will be in

the ratio 3 : 5

To find :

The present age of Raju and Rahul

Solution :

Let,

Present age of Raju = x years

Present age of Rahul = y years

Their ages before 4 year :-

⟶ Raju's age = (x - 4) years

⟶ Rahul's age = (y - 4) years

⟶ (x - 4)/(y - 4) = 3/8

⟶ 8(x - 4) = 3(y - 4)

⟶ 8x - 32 = 3y - 12

⟶ 8x - 3y = - 12 + 32

⟶ 8x - 3y = 20 -----(1)

Their ages after 5 years :-

⟶ Raju's age = x + 5 years

⟶ Rahul's age = y + 5 years

⟶ (x + 5)/(y + 5) = 3/5

⟶ 5(x + 5) = 3(y + 5)

⟶ 5x + 25 = 3y + 15

⟶ 5x - 3y = 15 - 25

⟶ 5x - 3y = - 10 -----(2)

Solving (1) and (2) :-

⟶ 8x - 3y = 20

⟶ 5x - 3y = - 10

⠀ (-)⠀ (+) ⠀⠀(+)

______________

⟶ 3x = 30

______________

⟶ 3x = 30

⟶ x = 30/3

⟶ x = 10

Substitute the value of x in equation (1) :-

⟶ 8x - 3y = 20

⟶ 8(10) - 3y = 20

⟶ 80 - 3y = 20

⟶ - 3y = 20 - 80

⟶ - 3y = - 60

⟶ 3y = 60

⟶ y = 60 ÷ 3

⟶ y = 20

Substitute the value of x and y in the assumed ages of Raju and Rahul :-

⟶ Raju's present age = x = 10 years

⟶ Rahul's present age = y = 20 years

Therefore,

• Present age of Raju is 10 years and Rahul is 20 years

Answer 2

Here is your answer Hope this will help you