Question

When ram will be as old as Ram's father is now, Ram will be five times as old as Ram's sons, at that time Ram's son will be eight years old than Ram is now. At the present , the sum of the age of Ram's father and Ram's is 100 years
1) How old is Ram's son?
2) How old would Ram have been five years ago?
3) After 10 years, how old will Ram's Father be?

Answer 1

Answer:

1)13 years

2)30 years

3)75 years

Answer 2

1) Ram's son is year old 13 years , (2)  Ram have been old  5 years ago 30 years and (3)   After 10 years, Ram's Father  will be years old  75 years.

Step-by-step explanation:

Given:

Ram's father  will become as old as Ram is now.

5 times Ram will be  as old as Ram's sons.

At that time Ram's son will be 8 years old than Ram is now.

The sum of  age is 100 years  of Ram's father & Ram's , at present.

To Find:

(1)  Ram's son is year old.

(2)  Ram have been old  5 years ago.

(3)  After 10 years, Ram's Father will be years old.

Formula Used:

If you are assuming the current age to be M, then the age after N years will be (M+N) years.

If you are assuming the current age to be M, then the age before n years will be (M-N) years

Solution:

Let the present age of Ram =P years  The present age of his son = Q years,  The present age of  Ram’s  father = R years.

As given - The sum of  age is 100 years  of Ram's father & Ram's , at present.

This means $P+R=100$               ---------------------------------- equation no.01

As given- 5 times Ram will be as old as Ram's sons.

This means   $R=5Q$                      ----------------------------------- equation no.02

As given - at that time Ram's son will be 8 years old than Ram is now.

This means   $Q+(R-P)=P+8$

                     $Q+R=2P+8$              --------------------------equation no.03

Putting the value of P  form equation no.01 to equation on.03, we get.

$Q+R=2(100-R)+8$

$Q+3 R=208$     Putting value of R from equation  no. 02 ,we get.

$Q+3(5 Q)=208$

$16 Q=208$

$Q=13$ years.

Putting value of Q in equation 02, we get.

$R=5\times 13=65$ years

Putting value of Q in equation no.01,we get.

$P+65=100$

$P=35$ years.

(1)  Ram's son is year old = 13 years

(2)  Ram have been old  5 years ago$=35-3=30$ years.

(3)  After 10 years, Ram's Father  will be years old $=65+10=75$ years.

Thus, (1) Ram's son is year old 13 years , (2)  Ram have been old  5 years ago 30 years  and (3)   After 10 years, Ram's Father  will be years old  75 years.