Question

Suma is 15 years older than Vivek. Three years from now, Suma’s age will be 8 times that of Vivek’s age 3 years back. What is the present age of Vivek?
A. 3 years
B. 6 years
C. 16 years
D. 17 years

Answer 1

Hint: According to the given question we have to find the present age of Vivek, when Suma is 15 years older than Vivek. Three years from now, Suma’s age will be 8 times that of Vivek’s age 3 years back.
So, first of all we have to let the present age of Vivek equals to $x$ years and according to the given condition that Suma is 15 years older than Vivek, we can get the age of Suma in the form of $x$.
Now, As per given condition in the question that three years from now, Suma’s age will be 8 times that of Vivek’s age 3 years back, we get the following expression as given below:
Expression obtained = present age of Suma $ + 3$= $8($present age of Vivek $ - 3)$……………………………..(A)

Complete step-by-step solution:
Step 1: first of all we have to let the present age of Vivek = $x$years
Now, as given in the question that Suma is 15 years older than Vivek
The present age of Suma will be = $\left( {x + 15} \right)$years
Step 2: Now, we have to use the expression (A) that is mentioned in the solution hint.
$ \Rightarrow \left( {x + 15} \right) + 3 = 8\left( {x - 3} \right)$
Now, simplify the above expression obtained
$
   \Rightarrow x + 18 = 8x - 24 \\
   \Rightarrow 8x - x = 24 + 18 \\
   \Rightarrow 7x = 42 \\
   \Rightarrow x = 6
 $
Step 3: Hence, the present age of Vivek will be = $x = $6 years
The present age of Suma will be = $\left( {x + 15} \right)$
$
   \Rightarrow \left( {6 + 15} \right) \\
   \Rightarrow 21
 $
Final solution: Hence, the present age of Vivek is 6 years.

So, the option (B) is correct.

Note: It is necessary that we have to let the age of the Vivek be x years and then as given in the question that sum is 15 years older than Vivek so that the age of Suma will be $x + 15$ years.
After 3 years the age of Suma is 8 times of Vivek three years before, so we can determine the value of x with the help of the expression which is the age of Vivek.