Question

If before three years, the sum of ages of father and son was 59 years, then before five years, the sum of their ages would have been ___________
(a) 55
(b) 61
(c) 69
(d) 57

Answer 1

Hint: We are given that the sum of ages of the father and son 3 years ago was 59. We will first assume their present ages as x and y. Then we have to find the age of them 5 years before. So, 3 years before, it will be (x – 3) and (y – 3). So we will find x + y and use it to solve further.

Complete step-by-step answer:
Let the present age of the son and father be x years and y years respectively.
So, 3 years ago,
Age of Son = (x – 3) years
Age of Father = (y – 3) years
We are given that the sum of the ages 3 years ago was 59 years. So, we get,
\[\left( x-3 \right)+\left( y-3 \right)=59\]
\[\Rightarrow x+y-3-3=59\]
\[\Rightarrow x+y-6=59\]
\[\Rightarrow x+y=59+6\]
\[\Rightarrow x+y=65......\left( i \right)\]
So, we get the sum of the ages of son and father as 65.
Now, 5 years ago,
Age of Son = (x – 5) years
Age of Father = (y – 5) years
Now, we have to find the sum of their ages. So, we get,
\[\left( x-5 \right)+\left( y-5 \right)\]
\[\Rightarrow x-5+y-5\]
\[\Rightarrow x+y-10\]
\[\Rightarrow \left( x+y \right)-10\]
Substituting the value of (x + y) from (i), we get,
\[\Rightarrow 65-10\]
\[\Rightarrow 55\]
Hence, we get the sum of the ages of the father and the son 5 years before as 55 years.
Hence, option (a) is the right answer.

Note:While opening the brackets (x – 5) + (y – 5), we should be very careful as careless mistakes like x – 5 + y + 5 can occur. While moving the terms around the ‘=’ always change the sign as sometimes it can cause a major error in the solution.