Aptitude - Problems on Ages - Discussion

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.

Hey guys.

Can I know how is that 5 (x+8) has written, Anyone please explain me?

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.

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.

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.

Gr8 Yuga!

Can somebody explain the Actual calculation presented by them?

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.

Hey but does x=40 means after 8 years. They have asked for present age. Doesn't it should be x=32, the present age ?