Aptitude - Problems on Ages - Discussion

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.

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.

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.

Let Mother Present age = x

Person age = (2/5)x

After 8 Years Persons Age Will be = (2/5)x + 8

After 8 Years Mother Age Will Be x + 8

Given That After 8 years, Person will be one-half of the age of his mother.

Here One-Half Means 3/2 actually . (But He Take 1/2 in the Explanation . So let we take 1/2).

(2/5)x + 8 = (1/2)(x+8).

(2x + 40)/5 = (x+8)/2.

4x + 80 = 5x + 40.

x = 40.

Mother Present Age x = 40.

Present Let mother age :X.
Person's age :2/5x.
After 8 years.

Then it converted into the present.

So.
Mother age:x-8.
Person age:2/5 (x-8).
He/person will be one-half of the age of his mother.
2/5 (x-8) = 1/2 (x-8)--->(1).

By solving equation (1) you can directly get an answer.

Why because we already feature/aftet8 yers converts into the present.

So,

X=40.

Hii.

Let present age of man = x and that of mother = y.

Then, x = 2/5y....equation....(1).

After 8 years, x+8 = 1/2(y+8).

x+8 = 1/2*y+1/2*8.
x+8 = y/2 + 4.

Substituting the value of x in equation....(1) we get,

2/5y+8 = y/2+4.
2y+40/5 = y+8/2.

On cross multiplication we get.

4y+80 = 5y+40.
4y-5y = 40-80.
-y = -40 or y = 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

ONE HALF is the irreducible fraction resulting from dividing one by two (½), or any number by its double; multiplication by one half is equivalent to division by two. It appears often in mathematical equations, recipes, measurements, etc. Half can also be said to be one part of something divided into two equal parts.

We can solve it in ratio method,

Present age=P : M =2:5
Age after 8 yrs=P(8):M(8)=1:2,
To equalise the difference we multiply both the numbers with there differences=2:5*1,1:2*3
We get, 2:5
3:6
The difference of both the numbers is equal that is 1.
1=8,
5=8*5 = 40yrs,
Mother's age is 40 yrs.

Let mother's age = 5x,
So person's age will be 2/5 * 5x = 2x,
So the ratio of son and mother will be = 2x : 5x,

Note: One-half means only half and one and half mean 3/2.

After 8 years:
(2x + 8) = 1/2 * (5x + 8),
2(2x + 8) = (5x + 8),
4x + 16 = 5x + 8,
x = 8.
Now mother's present age = 5 * 8 = 40.