Aptitude - Problems on Ages - Discussion

Three times parents age of a father is equal to eight time age of his son. Eight years hence the father will twice as old as his son at that time. What are the parent ages?

Can any body solve this question?

Let,

Father = X.
Ronit = Y.

1st case:
X = 3Y.

2nd case:
X+8 = Y/2.

Third case:
X+16 = Y.

2X+16 = 3Y. From 1st and second case.

Then subtract third case in it. You will get,

X=2Y.

@Newbie.

You made a wrong calculation 3*16 = 48 and 52+16 = 68.

For all your folks let me tell my method.

First he has given father's age is 3 times of rohit so if rohit age 1, then his fathers will be 1+3=4 i.e. the ratio will be 4:1.

Now after 8 years the ratio given is (2.5) :1.

Now 4-1=3.

2. 5-1=1. 5 for my method you have to keep the difference in two ratios must be same, so multiply (2.5) :1 with 2. It becomes 5:2 i.e. 5-2 = 3 the difference is same as of 4-1=3 now remember we got 5:2 after 8 years i.e 4:1.

8 years hence 5:2

Now 5-4=1= 8 years.

So that makes 40:16.

After further 8 years 48:24 i.e.TWISE (2 times).

Let Ronit's age = x.

Father's age = x+3x (three times more than his son Ronit) = 4x.

After 8yrs.

Ronit's age = x+8.

Father's age = 4x+8.

But father will be two and a half times of Ronit's age so.

4x+8 = 5/2 (x+8).

x = 8.

Further after 8 years.

Ronit's age = x+8+8 = x+16.

Father's age = 4x+8+8 = 4x+16.

We know the value of x is 8 so putting value of x.

Now,

Ronit's age = x+16=8+16=24.

Father's age = 4x+16 = 4*8 +16 = 32+16 = 48.

Now we will calaulate the ratio of father's to ronit's age.

Father's age/ronit's age = 48/24 = 2.

Thus 2 is answer.

2 and a half means 2*1/2 is simplified 2*2=4, and 4+1=5 is come 5/2.

@Poonam And @Thara in question this given that two and half.

Means 2and half which is 2.5 and 5/2 is same equal to 2.5.

Don't get confused in 2/5 and 2.5. Because 2/5 is .4 not 2.5.

Fathers age is 3 times more than his son 4x.

But after getting full stop considering and comparing other sums I can understand like this (x+8). How we put (4x+8) in fathers age?

And as @newbie said, if its correct then I am failing to understand that why is 3x + 8 = 2.5 x ? Shouldn't it be 3x + 8 = 2.5 (x + 8), because even the son's age should have been added to 8 right ?

It doesn't make sense why ppl take the fathers age as 4X just becos its says 'times more' . what if the son's age is 'times less' of the father? :D

So I made a calculation based on logic and it comes to this
son's age = x.
Father's age = X x 3 = 3X.

After 8 years father is 2 and half years older than his son, so if we add 8 years to the fathers age it will be equal to 2 and a half times of the son's age.

i.e 3X + 8 = 2 and a half times of X.
3X + 8 = 2 1/2 x X.

From the equation X = 16.

Now the fathers initial age = 3X.
= 3 x 16 (X=16).
= 52.

After 16 years (8+8 years) father will be,
= 52 + 16.
= 64.

In the same way the son after 16 years will be,
= X + 16.
= 16 + 16 = 32.

Hence the difference of their age will be, 64 divided by 32
= 64 / 32.
= 2.

So the Father will be 2 times older than the son in 16 years :D.