Question

Aman’s present age is two times the age of Varun. Also, the sum of both ages is eight less than fifty. Find their present ages.

Answer 1

Hint: In the given question, we are required to write an algebraic equation based on the information given to us. First, break down the information given to us to try and identify what an algebraic equation must look like. We will introduce some variables and form an algebraic equation and then try to solve the equation using the transposition method.

Complete step by step solution:
In the question, we are given that Aman’s age is twice of Varun’s age. So, we will introduce a variable and let the age of Varun be $x$.
Then, age of Aman $ = 2x$
Also, we are given that the sum of their ages is eight less than fifty.
So, we know that eight less than fifty is $50 - 8 = 42$.
So, we get,
$2x + x = 42$
Simplifying the equation, we get,
$ \Rightarrow 3x = 42$
Dividing both sides of the equation by three, we get,
$ \Rightarrow x = 14$
Therefore, Aman’s age is $14$ years. So, Varun’s age is $28$ years.

Note:
When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combinations of mathematical symbols is called a mathematical expression. If there is an equal $\left( = \right)$ sign in the expression, then it is called an equation. Method of transposition can be used to solve any mathematical equation.