Question

The sum of the age of Radha and Rani is 81 years. The ratio of their age is \[4:5\] respectively. What is Radha’s age?

Answer 1

Hint: Here, we will first assume that the age of Radha is \[4x\] and the age of Rani is \[3x\]. Then we will find the sum of the ages to form the equation and then solve the obtained equation. Then we will substitute the value of \[x\] in one of the ages to find the Radha’s age.

Complete step by step answer:

We are given that the sum of the age of Radha and Rani s 81 years and the ratio of their age is \[4:5\].

Let us assume that the age of Radha is \[4x\] and the age of Rani is \[5x\].

We will find the sum of the ages by adding the above ages and take it equal to 81, we get
\[
   \Rightarrow 4x + 5x = 81 \\
   \Rightarrow 9x = 81 \\
 \]
Dividing the above equation by 9 on both sides, we get
\[
   \Rightarrow \dfrac{{9x}}{9} = \dfrac{{81}}{9} \\
   \Rightarrow x = 9 \\
 \]
Substituting the value of \[x\] to find the age of Radha, we get
\[ \Rightarrow 4 \times 9 = 36{\text{ years}}\]

Thus, the age of Radha is 36 years.

Note: Whenever we face such type of questions on age problems, we always first suppose the age ratio with some variable \[x\] and then apply the conditions of the question on that variable to find out the value of that variable to find the result. Do not assume the value of \[x\] is the required answer, we have to substitute the value of \[x\] in one of the ages to find the final age, or else the answer will be incomplete.