Question

Sara’s age is 40% of Geeta’s age and Geeta’s age is 30% of Rohan’s age. What percent of Rohan’s age is Sara’s age?

Answer 1

Hint: We start solving the problem by assigning the variables for the ages of Geeta, Sara, and Rohan. We then use the property that a% of b is $\dfrac{a}{100}\times b$ for finding the relation between the ages of Sara and Geeta, also the relation between the ages of Geeta and Rohan. We then solve both the equations to get the relation between the ages of Sara and Geeta which will give us the required percentage.

Complete step-by-step solution
According to the problem, we are given that Sara’s age is 40% of Geeta’s age and Geeta’s age is 30% of Rohan’s age. We need to find what is the percent of Sara’s age in Rohan’s age.
Let us assume Sara’s age be ‘S’, Geeta’s age be ‘G’, and Rohan’s age is ‘R’.
We have given that Sara’s age is 40% of Geeta’s age. So, we get S = 40% of G.
We know that a% of b is defined as $\dfrac{a}{100}\times b$. So, we get $S=\dfrac{40}{100}\times G$.
$\Rightarrow S=0.4G$ ---(1).
Now, we have given that Geeta’s age is 30% of Rohan’s age. So, we get G = 30% of R.
We know that a% of b is defined as $\dfrac{a}{100}\times b$. So, we get $G=\dfrac{30}{100}\times R$.
$\Rightarrow G=0.3R$ ---(2).
Let us substitute equation (2) in equation (1).
So, we get $S=0.4\times \left( 0.3R \right)$.
$\Rightarrow S=0.12R$.
$\Rightarrow S=\dfrac{12}{100}\times R$.
So, we get S = 12% of R.
We have found that Sara’s age is 12% of Rohan’s age.

Note: Whenever we get this type of problem, we should assign the variables for the unknowns present in the problem to avoid confusion while solving the problem. We should not confuse a% of b with $a\times b$ instead of $\dfrac{a}{100}\times b$. We should confuse and find the percent of Rohan’s age with Sara’s age. Similarly, we can expect problems to find by how much percentage the Rohan’s age is when compared to Sara’s age.