Aptitude - Problems on Ages - Discussion

But here, it did not specify whether the mothers age also adjusted. I think this is how you should have phrased this part. "After 8 years, he will be one-half of the age of his mother THEN". Notice the word then, it makes it much clearer.

You are right @Kinyera.

If we take 3/2 the answer will be 10.

I think the question is incorrect.

Guys are saying that one-half means 1/2 then how will you express just "half"?

The person present age is 2/5 of his mom.

2/5 son = mom hence, 2 (son age) = 5 (mom age) , taking 5 to other side 2:5.

After 8 years: so will be 1/2 of mother =1/2 (son age) = mom.

1 (son age) = 2 (mom age) taking 2 to other side 1:2.

Since it is after 8 years you can convert in to present, so subtract 8.

General formula.

Present = 2:5, after 8 years = 1:2.

2x-8/5x-8 = 1/2 (then cross multiplication).

This gives 2 (2x-8) =1 (5x-8).

4x-16 = 5x-8.

4x-5x =16-8.

(x=8).

So mom present age is 5x.

5*8 =40 ; so mom present age is 40.

Is it clear.

I have one doubt please tell me.

They asked about present age but we have added 8 years. How it will be the present age?

Ratio of a:b is always written as ax & bx.

So here ratio of persons age and mothers age is 2:5 i.e, two-fifth which will be 2x & 5x.

They have given after 8 years so we need to add 8 in both values and ratio after 8 years is 1:2, so it will be:

2x+8/5x+8 = 1:2.

(Cross multiply-(2x+8*2)(5x+8*1)).

4x+16 = 5x+8.

X = 8.

So, the mother age is 5x i.e. insert x value.

5*8 = 40.

Therefore mothers age is 40 years.

Why should it can't be 32 there is a possibility to get 32 as a answer?

Can anyone give clear explanation about this?

Hey please someone tell me why they have taken LCM only one side.

2X/5+8 = 1/2x+8.

It should be like this: 2x+40/5 = x+16/2.

Please give simple solution and tricks.

Simple method.

If mother is twice of son then only son will be half of age of mother.

Means if mother is 10 yrs, then son is 5 years. Or in other words if son is of 5 years than mother will be 5*2 = 10 years.

Now come to the question.

Suppose mother present age is x.
Son present age is 2/5x.
After 8 years.

Mother age is x+8.
Son age is 2/5x+8.

Now son is half of mother age means mother is twice of son age.

So mother age after 8 years = 2*son age after 8 years.

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

After taking L.C.M. of bracket we will have.

5(x+8) = 2(2x+40).
5x+40 = 4x+80.
x = 40 years.