Question

The age of Tarun is one-third the age of his mother. If the sum of their ages is 48, find the age of Tarun.

Answer 1

Hint: We will form the equations based on the conditions given in the question. After having the equations, we will try to link both of them, and will replace one equation in purely one variable, to get its value. Then we will substitute the obtained value into any one of the formed equations, to find the required value.

Complete step by step Answer :

Let us take the age of Tarun to be x and that of his mother to be y.
According to the given question, the age of Tarun, which is x, is one-third the age of his mother, which is y.
$\Rightarrow x = \dfrac{1}{3}y$ ……(1)

Now further it is given in the question that the sum of their ages is 48, that is, the sum of x and y is 48.
$\Rightarrow x + y = 48$ ……(2)

Now, substitute the value of x from equation (1) into equation (2) to find the value of y, which is the age of Tarun’s mother.
$\Rightarrow \dfrac{1}{3}y + y = 48 \\\ \Rightarrow \dfrac{{1y + 3y}}{3} = 48 \\\ \Rightarrow 4y = 3 \times 48 \\\ \Rightarrow y = 3 \times 12 \\\ \Rightarrow y = 36 \\\$

As, we are required to find the age of Tarun, which is given by x, thus, we substitute this obtained value of y into the equation (1).
$\Rightarrow x = \dfrac{1}{3} \times 36 \\\ \Rightarrow x = 12 \\\$

Hence, the age of Tarun is 12 years.

Note: While choosing the variable, be careful to mention them, in order to avoid the mixing of them with each other. Also, form the equations, based only on the given conditions and no intuitions. Make sure to use the same variable assigned at the beginning of the question, throughout your solution. Also, while substitution, make sure you do not make any calculation errors. Also, you should be familiar with the terms, like one-third, half, quarter etc in order to easily solve these questions.