Question

2n years ago the age of Raju was 4 times that of his son and n years ago the age of Raju was thrice that of his son. If n years later, the sum of the ages of Raju and his son will be 80 years then the difference in the ages of Raju and his son is

Answer 1

Answer:

here your answer.........

30 year's

Step-by-step explanation:

let the ages of Raju and his son is

a and b respectively.

then difference between Raju and his

son is (a-b)

As per first condition 2n year's ago

their ages

a-2n=4(b-2n)

a-2n=4b-8n

a=4b-8n+2n

a=4b-6n........................................ (1)

And second condition

n year's ago,

a-n=3(b-n)

a-n=3b-3n

a=3b-3n+n

a=3b-2n.............................................. (2)

Substract equations (1) -(2)

we get

4b-6n-3b+2n=0

b-4n=0

b=4n.

now substitute b value in equation (1)

a=4×4n-6n

a=16n-6n

a=10n.

As per third condition after n year's,

a+n+b+n=80................................... (R)

put a and b values in equation (R)

10n+n+4n+n=80

16n=80

n=80/16

n=5

the age of Raju is a=10n=10*5=50.

and his son age is b=4n=4*5=20.

therefore the difference between the

ages of Raju and his son is

a-b=50-20=30.