Aptitude - Problems on Ages - Discussion

Suppose, the mother's age is 100 years and person's age has two-fifth of his mother then two-fifth of 100 is 40 years.

2/5 * 100 = 40.

@Aditya Ive solved it this way....

The ratio of the person's and his mother's present age is 2:5.
Therefore, take the person's age as 2x and his mother's age as 5x.

After 8 years[(add 8 to both values)...i.e. (2x+8) and (5x+8)] their age ratio is 1:2.


Hence,
(2x+8)/(5x+8)=1/2
4x+16=5x+8
x=8

So, the mother's age=5*8=40

They are asking the present age of the mother.

So, the answer could be 32 only.

If we suppose mothers age as 40 then son's age will be 16years according to 2/5th part. Then after 8years son's age will be 24years and mothers age is. 48years. This is also half of the mother. Then this is also correct only, right? Please correct me, if I am wrong.

The correct answer would be 32 as it is mentioned in the question the present age, so it must be 40-8=32.

Thank You for explaining @Yuga.

Question says one-half of the age, Not one and half.

So,It's 1/2 not 3/2.

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.

Let mother 's age be x.
2/5x + 8 = 1/2(x+8),
0.4x + 8 = 0.5(x+8),
X = 40.

Thanks @Yuga.