Question

Soni’s brother is 8 years older than the four-fifth of her age. If her brother’s age is 32 years, then find the age of Soni?

Answer 1

Hint: We start solving the problem by assigning the variable for the Soni’s age. We then multiply this variable with $\dfrac{4}{5}$ in order to get the four-fifth of her age. We then add 8 years to the obtained result to get 8 years older than the four-fifth of her age. We equate the obtained result with his brother’s age given in the problem. We then make necessary calculations required to get Soni’s age.

Complete step-by-step answer:
According to the problem, we are given that Soni’s brother is 8 years older than the four-fifth of her age. We need to find the age of Soni if the age of her brother is given as 32 years.
Let us assume the age of the Soni is x years.
We need to find the four-fifths of Soni's age. So, we multiply x with $\dfrac{4}{5}$ to get the four-fifth of the age of Soni.
So, the fourth-fifth of Soni’s age is $\dfrac{4}{5}x$ years. Now, we need to add 8 years to $\dfrac{4}{5}x$ years in order to get the age 8 years older than the four-fifth of her age. So, this makes us get the age as $\dfrac{4}{5}x+8$ years.
But this is equal to the age of his brother which is 32 years.
So, we have $\dfrac{4}{5}x+8=32$.
$\Rightarrow \dfrac{4}{5}x=32-8$.
$\Rightarrow \dfrac{4}{5}x=24$.
$\Rightarrow 4x=24\times 5$.
$\Rightarrow 4x=120$.
$\Rightarrow x=\dfrac{120}{4}$.
$\Rightarrow x=30$ years, which is the age of Soni.
So, we have found Soni’s age is 30 years.
∴ The age of Soni is 30 years.

Note: Whenever we get this type of problems, we should start by assigning variables to the unknowns to avoid confusion while doing the calculations. We should keep in mind that the person is older than others if his/her age is greater than the other. We can verify by doing back calculation after finding the age of Soni. Similarly, we can expect problems which are needed to find the age of both persons.