Question

Ahmad is 7 years older than John. Four years ago, Ahmad was twice as old as John. Find the sum of their ages in 7 years time.
(a) 37 years
(b) 43 years
(c) 60 years
(d) 52 years

Answer 1

Hint: We have been conditioned to ages of john and ahmad. We need to solve the conditions for the present ages of the john and ahmad. And then we have to give the sum of their ages after 7 years.

Complete step-by-step answer:
We have to find the sum of the ages of Ahmad and John after 7 years.
For that, we need to find the present ages of ahmad and john.
Let the present age of john be $x$ years.
According to the condition, Ahmad is 7 years older than john.
Therefore, the present age of ahmad will be $\left( x+7 \right)$ years.
The second condition given is four years ago.
So, four years ago the age of john was $\left( x-4 \right)$ years.
And four years ago the age of Ahmad was $\left( x+7 \right)-4$ years =$\left( x+3 \right)$ years.
The condition says that four years ago, Ahmad was twice as old as john.
By equation we get,
$\left( x+3 \right)=2\left( x-4 \right)...........(i)$
Simplifying the equation and solving for $x$ we get,
$\begin{align}
  & x+3=2x-8 \\
 & \Rightarrow x-2x=-3-8 \\
 & \Rightarrow -x=-11 \\
 & \Rightarrow x=11 \\
\end{align}$
Therefore, the present age of john is 11 years.
From the first condition, the present age of ahmad is 11 + 7 = 18 years.
We have asked the sum of the ages after 7 years.
After 7 years, the age of john will be 11 + 7 = 18 years.
After 7 years, the age of ahmad will be 18 + 7 = 25 years.
Therefore, the sum ages of john and ahmad after 7 years is 25 + 18 = 43 years.
Hence, the correct option is (b).

Note: Even if we have calculated the value of $x$ from the condition 4 years ago the age we get is the present age of John due to our initial assumption. Also, the common missout point is that the sum of ages is asked after 7 years and not the sum of the present ages. In the second condition, Ahmad is twice as old as John after 4 years. So, we need to multiply 2 on the side of John to maintain equality.