Question

Suresh is half his father’s age. After $20{\text{ years}}$, his father’s age will be one and a half times the Suresh’s age. What is his father’s age now?
A. $40$
B. $20$
C. $26$
D. $30$

Answer 1

Hint: Here we can suppose the present ages of the father of Suresh be$x{\text{ years}}$ and accordingly we can find the present age of Suresh as his present age is half of this father’s age. Then we can form another equation by taking their ages after $20{\text{ years}}$ as $\left( {x + 20} \right){\text{ years and }}\left( {\dfrac{x}{2} + 20} \right){\text{ years}}$.
Then form another equation and solve for $x$.

Complete Step by Step Solution:
Here we are given that Suresh is half his father’s age.
Therefore let us suppose that present age of Suresh’s father be $x{\text{ years}}$
Now the present age of Suresh will be $\dfrac{x}{2}{\text{ years}}$
After $20{\text{ years}}$ theirs ages will be $20$ more than their present ages which we have let earlier.
So we can say after $20{\text{ years}}$
Father’s age$ = \left( {x + 20} \right){\text{ years}}$
Suresh’s age$ = \left( {\dfrac{x}{2} + 20} \right){\text{ years}}$
Now it is also said that after $20{\text{ years}}$father’s age is one and a half times his son, Suresh’s age.
So we can say that after $20{\text{ years}}$
${\text{father's age after 20 years}} = \dfrac{3}{2}\left( {{\text{Suresh's age after 20 years}}} \right)$
Hence we will get:
$\left( {x + 20} \right) = $$\dfrac{3}{2}\left( {\dfrac{x}{2} + 20} \right)$
Now we can solve it and we will get:
$
  x + 20 = \dfrac{{3x}}{4} + 30 \\
  x - \dfrac{{3x}}{4} = 30 - 20 \\
  \dfrac{x}{4} = 10 \\
  x = 40 \\
 $
Hence we can say that:

Present age of father$ = x = 40{\text{ years}}$

Note:
Here the student can also suppose both the ages as the two separate variables and then form two equations and solve for both the variables as we will have two equations and two variables.