Three years ago, the ratio of the ages of a father and a son was 6:1.

Question

Three years ago, the ratio of the ages of a father and a son was 6:1. After 3 years, the ratio will be 36:11. Find the present age of the son.

(A) 3 years 
(B) 5 years
(C) 8 years 
(D) 11 years
(E) 17 years

Nidzo · Answer

Slightly confusing, but the question gives you the ratio 3 years before the present day and 3 years after the present day. This means that there are 6 years between the given ratios.

(6x+6)/(x+6) = 36/11
66x + 66 = 36x + 216
30x = 150
x = 5

Which means that the present day age of the boy is  5+3=8

Answer C

Showmeyaa · Answer

Let 3 years ago the father and son age be 6x and x respectively.
Present ages will be 6x + 3, and x + 3 respectively.
After 3 years,  \frac{6x + 6}{x + 6} = \frac{36}{11} 
66x + 66 = 36x + 216
30x = 150
x = 5
Present age of son = x + 3 = 5 + 3 = 8, (C) IMO!

GMATWhizTeam · Answer

Solution:

It is given that 3 years ago, the ratio of the ages of a father and a son was  6:1 . 
So, we can assume the age of father and son 3 years ago =  6x  and  1x  years.

So, present age of father =  6x+3 
Present age of son =  1x+3 .

Age of father 3 years after today =  6x+6 
Age of son 3 years after today =  x+6

We are given:  \frac{6x+6}{x+6}=\frac{36}{11} 
 ⇒ 11(6x+6)=36(x+6)  (cross multiplying)
 ⇒ 66x+66=36x+216 
 ⇒ 66x-36x=216-66 
 ⇒ 30x=150 
 ⇒ x=150/30 
 ⇒ x=5

Present age of son  = x =5 years.

Hence the right answer is  Option C .

Nikitha16 · Answer

Let the current age of father and son be f and s.

Three years ago(ie f-3 and s-3) are in the ratio 6:1 => (f-3) : (s-3) = 6:1;
On solving we get, f = 6s-15;

After 3 years(f+3 and s+3) are in the ratio 36:11 => (f+3) : (s+3) = 36:11;
On solving we get, 11f = 36s+75;

Substitute f = 6s-15 into 11f=36s+75, on solving we get s = 8, which is the required answer.

CrackverbalGMAT · Answer

In questions on ages, always assume the ages of the persons using variables. Also, take a reference situation to assume the variables (current age / 3 years ago / 2 years hence etc.,)

Three years ago, let the ages of the father and the son be 6k and k.

After three years, their ages will be 6k + 6 and k+6, which are in the ratio of  \frac{36 }{ 11} 
(Note that our reference variables are for 3 years ago, therefore, we need to add 6 to each of them to get the variables for 3 years later)

\frac{6k + 6 }{ k + 6} = \frac{36 }{11} .

Simplifying and solving the above equation for k, k = 5. 
Beware of trap answer option B; remember that we want the present age of the son and k does not represent the present age.

Present age = k + 3 = 8 years.

The correct answer option is C.

Hope that helps!
Aravind B T

CrackverbalGMAT · Answer

Hello GMATWhiz,

You may want to correct the last part of your answer explanation - the present age is 8 years, which is x+3 and not x.

You have highlighted the correct answer option though!

Hope that helps!
Aravind B T

Hariharan1 · Answer

Six years ago, let age of father be f and son be s .
f= 6s.'
Age ratio after 6 years is = (f+6)/(s+6) = 36/11
replace f=6s
so 6(s+1)/(s+6) = 36/11
(s+1)/(s+6) = 6/11
so, s has to be 5.As per calculation
That means s+3 = 8.
Son's current age is 8.

anandprk · Answer

After 3 years, ages of dad/son respectively can be 36/11 or 72/22 and so on (since all answer choices are integers.)
Looking at the choices, only 8 can be the current age of the son. 
 Hence, C

Posted from my mobile device

bumpbot · Answer

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Three years ago, the ratio of the ages of a father and a son was 6:1.

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