Question

40. Four years ago, the age of Gopal was thrice the age of Ram. After 4 years, the age of Gopal would be double
the age of Ram. Find their present ages. ​

Answer 1

Step-by-step explanation:

Given :-

Four years ago, the age of Gopal was thrice the age of Ram. After 4 years, the age of Gopal would be double the age of Ram.

To find :-

Find their present ages ?

Solution :-

Let the present age of Gopal be X years

Let the present age of Ram be Y years

Four years ago their ages were

(X-4) years and (Y-4) years

Age of Gopal 4 years ago = (X-4) years

Age of Ram 4 years ago = (Y-4) years

Given that

Four years ago, the age of Gopal was thrice the age of Ram

=>(X-4) = 3(Y-4)

=>X-4 = 3Y-12

=> X = 3Y-12+4

=> X = 3Y-8 ------------------(1)

After 4 years their ages will be (X+4) years and

(Y+4) years

Age of Gopal after 4 years = (X+4) years

Age of Ram after 4 years = (Y+4) years

Given that

After 4 years, the age of Gopal would be double

the age of Ram.

=> X+4 = 2(Y+4)

=> X+4 = 2Y+8

=> X = 2Y+8-4

=>X = 2Y+4

From (1)

=> 3Y-8 = 2Y+4

=> 3Y-2Y = 4+8

=> Y = 12

and

From (1)

=> X = 3(12)-8

=> X = 36-8

=> X = 28

Therefore,X = 28 years and Y = 12 years

Answer:-

The present age of Gopal = 28 years

The present age of Ram = 12 years

Check:-

Gopal = 28 years

Ram = 12 years

4 years ago their ages

Gopal = 28-4 = 24 years

Ram = 12-4=8 years

Gopal = 3×8 = 24 years

Gopal 's age is thrice the age of Ram

And

4 years after

Gopal = 28+4=32 years

Ram = 12+4=16 years

Gopal = 2×16=32 years

Gopal 's age is double the age of Ram

Verified the given relations in the given problem.

Used Method:-

Substitution method