Aptitude - Problems on Ages - Discussion

Consider son's age as 'x'.

So they have said,
Father is aged three times more than his son.

As per the statement, x+3x.
After 8 years, he would be 2 and a half times of his son.

So, x+3x+8 = x+8.
4x+8 = x+8.
(4x+8) = 5/2(x+8).

We get, 8x+16 = 5x+40 => 3x = 24.
x = 8.

After further 8 years,

So add 8 to the equation 4x+8+8 = x+8+8.
4x+16 = x+16.

So the ratio is, (4x+16)/(x+16) = 48/24.
=> 2 years.

Got it friends. Its simple?

Let Ronit's age = x.

So father's age will be (x+3x), (Let suppose you have sister who is 1 year younger than you then after 20 year your age will be 21 (Your sister age + 20 yr) = your age. So same in this question father age will be x+3x.

Now after 8 years mean rule no.2 (If x is current age then n year later age will be (x+n)).

Father's age will be (4x+8) and Ronit's age will be (x+8).

Now come to question that after 8 years father's age will be 5/2 times of Ronit's age.

So F age = 5/2 times of Ronit's age.

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

So by this we get x = 8.

Now we have to find after 8 year.

= 4x+8+8 = y(x+8+8).

So by solving this y = 2.

Thank you :).

Any other short way to solve this question?

How can such a question be solved with in one minute?

Please explain the concept of solving this problem using shortcut method.

(4x + 8) = 2.5(x + 8).

4x + 8 = 2.5x + 20 and equation multiplied by 2.

2 and 1/2 == 5/2.

Since given "of Ronit's age", therefore multiply 2/5 to Ronit's age.

I think answer is 2.2 times.

x = son Ronit's age now.

3x = father's age now <--- father is 3 times son.

x + 8 = Ronit's age in 8 years.

3x + 8 = father's age in 8 years.

3x + 8 = 2.5 (x + 8) <--- after 8 years, father is 2.5 times son.

3x + 8 = 2.5x + 20 <--- used distributive property.

0.5x = 12 <--- subtracted 2.5x and 8 from each side.

x = 24 <--- divided each side by 0.5.

3x = 72 <--- substituted 24, in for x, into 3x.

Son Ronit is 24 now & father is 72 now.

Son Ronit will be 32 in 8 years & father will be 80 in 8 years.

Son Ronit will be 40 after further 8 years & father will be 88 after further 8 years.

Father will be 2.2 times son after further 8 years.

The last step is easy but division sign gone somewhere else. Fathers age is 4X + 8 + 8 (here 8 + 8 are the years later) now divide this with sons age which is x. But after 8 + 8 years it would be x + 8 + 8 as we got x value substitute in the both numerator and denominator there you go you get as 48/24 and we taking in ratio forms as options are given in ratio like two times the son age etc.

How it is 4x?

Father's age is three times more than his son's age means. We can say (3x+x) or (3x+2x)...

Why we take it as (x+3x)?