Question

A is 25 years older than B. In 15 years, A will be twice of B. Find the present ages of A and B.
A. Present age of A is 40 years and Present age of B is 15 years
B. Present age of A is 37 years and Present age of B is 12 years
C. Present age of A is 35 years and Present age of B is 10 years
D. Present age of A is 45 years and Present age of B is 20 years

Answer 1

Hint: We will first start by assuming the present ages of A and B as x and y respectively. Then we will use the fact that A is 25 years older than B to form an equation. Then we will use the fact that in 15 years A will be twice the b to form another equation. We will solve both these equations for the values of x and y to find the answer.

Complete step-by-step solution -
Now, we let the present ages of A = x years
we have the present ages of B = y years
Now, we have been given in the question that A is 25 years older than B. So, we have,
$x=25+y......\left( 1 \right)$
Also, we have been given that in 15 years A will be twice of B. So, we have,
$\left( x+15 \right)=2\left( y+15 \right)...........\left( 2 \right)$
Now, we substitute x from (1) and (2). So, we have,
\[\begin{align}
  & \left( 25+y+15 \right)=2\left( y+15 \right) \\
 & 40+y=2y+30 \\
 & 40-30=2y-y \\
 & 10=y \\
 & y=10years \\
\end{align}\]
Now, we substitute y = 10 in (1). So, we have,
$\begin{align}
  & x=25+10 \\
 & =35years \\
\end{align}$
So, the present age of A and B are 35 and 10 years respectively.
Hence, the correct option is (C).

Note: It is important to note that we have used the elimination method of solving the system of equations in two variables. Also, it is important to note that we have first let the ages which we have to find and then formed the equations as per the conditions given in the question.