Aptitude - Problems on Ages - Discussion

Can anybody explain me?

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

4x + 80 = 5x + 40.

2x/5+8/1 = 1/2(x+8).
(here we are going to cross multiply 5*8 = 40).

2x = 40/5 = 1/2(x+8).
2x = 40/5 = 1/2(x+8).

4x+80 = 5x+40.
Then x = 80-40.

= 40.

Hope you got it.

In question they have asked present age of mother, But 40 is after 8 years old. Shouldn't it be 40-8-32?

Can any one explain me - one half means 3/2 or 1/2 - if exactly one-half means 3/2 means- why they taken it as 1/2 while solving - please explain me about the difference of both?

Second step how wrote by first line?

Person mother.

2 5.

1 2 (8 year hence).

Then mother's present age is.

M = (5*8*1)/(5*1) - (2*2).

M = 40.

How 59(x+8) came?

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.

Ratio of present age of mother and son is 5:2.

After 8 years ratio becomes 2:1.

So x = 8*(2-1)/5-4 = 8.

Mothers age is 8*5 = 40.

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.