Question

My age is two years less than twice of my brother. If I am sixteen year old, how old is my brother?
(A) 7
(B) 9
(C) 10
(D) 14
(E) 15

Answer 1

Hint: Assume that the age of my brother is \[x\] years. My age is equal to 16 years. Since my age is two years less than twice of my brother's, if we add two years to my age then it should be exactly equal to the age of my brother. Use this and form an equation. Now, solve it further and calculate the value of \[x\] .

Complete step-by-step answer:
First of all, let us assume that the age of my brother is \[x\] years ………………………………..(1)
It is given that my age is 16 years ……………………………………………..(2)
Also, we are given that my age is 2 years less than twice of my brother.
From equation (1) and equation (2), we have my brother’s age and my age respectively.
Since my age is two years less than twice of my brother so, if we add two years to my age then it should be exactly equal to the age of my brother ……………………………………………(3)
From equation (1), equation (2), and equation (3), we get
\[\begin{align}
  & \Rightarrow 2x=16+2 \\
 & \Rightarrow x=\dfrac{18}{2} \\
\end{align}\]
\[\Rightarrow x=9\] ……………………………….(4)
From equation (4), we have the value of \[x\] and from equation (1), we have assumed that the age of my brother is \[x\] .
Therefore, the age of my brother is 9 years.

So, the correct answer is “Option A”.

Note: In this question, one can also form an equation as, \[2x-2=16\] . Since it is given that my age is 2 years less than twice of my brother’s age. So, 2 must be deducted from the twice of my brother’s age to make it equal to my age.