Aptitude - Problems on Ages - Discussion

Please give simple solution and tricks.

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.

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

Can anyone give clear explanation about this?

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.

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?

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.

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

You are right @Kinyera.

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

I think the question is incorrect.

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.

Let the mother present age = x.
Man's age = 2x/5.

x + 8 = 1/2 (2x/8 * 5),
x + 8 = 4x/16 * 5,
x + 8 = 4x/16 * 5,
x + 8 = 4x + 80/5,
5x + 40 = 4x + 80,
x = 40.