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: In this question, we are given relation between the ages of Sara and Geeta. Also we are given a relation between the age of Geeta and Rohan. We need to find the relation between the ages of Rohan and Sara. For this, we will assume Rohan's age as x and then find Geeta's age in terms of x. Using the age of Geeta, we will find the age of Sara in terms of x. At last, we will find what percent of Rohan's age is Sara's age using the formula \[\dfrac{\text{Sara }\!\!'\!\!\text{ s age}}{\text{Rohan }\!\!'\!\!\text{ s age}}\times 100\]. In this question, we will use a formula x% of y $\Rightarrow \dfrac{x}{100}\times y$

Complete step-by-step answer:
Here let us suppose that the age of Rohan is x years.
We are given that Geeta's age is 30% of Rohan's age then this means that Geeta's age is 30% of x. We know that, x% of y is equal to $\Rightarrow \dfrac{x}{100}\times y$.
So we can say that Geeta's age is $\Rightarrow \dfrac{30}{100}\times x$.
Now ... can be written as 0.3, so Geeta's age = 0.3x
Now, we are given that Sara's age is 40% of Geeta's age which means that Sara's age is 40% of 0.3x.
We know that, x% of y is equal to $\Rightarrow \dfrac{x}{100}\times y$.
Hence, Sara's age is equal to $\Rightarrow \dfrac{40}{100}\times 0.3x$.
Let us simplify $\dfrac{40}{100}\times 0.3$ first.
0.3 can be written as $\dfrac{3}{10}$ so we get:
$\dfrac{40\times 3}{100\times 10}=\dfrac{120}{1000}$.
Now $\dfrac{120}{1000}$ can be written as 0.12
So Sara's area is equal to 0.12x.
Now, we need to find what percent of Rohan's age is Sara's age. For this, we will use the formula \[\dfrac{\text{Sara }\!\!'\!\!\text{ s age}}{\text{Rohan }\!\!'\!\!\text{ s age}}\times 100\].
Since, Sara's age is found as 0.12x and Rohan's age was supposed as x. So we get: \[\dfrac{0.12x}{x}\times 100\].
Cancelling x from the numerator and the denominator we get:.$0.12\times 100$.
Now 0.12 can be written as $\dfrac{12}{100}$ so we get: $\dfrac{12}{100}\times 100=12$.
Hence the required percentage is 12%.

Note: Students often make mistakes of calculating percentage by writing the formula as \[\dfrac{\text{Rohan }\!\!'\!\!\text{ s age}}{\text{Sara }\!\!'\!\!\text{ s age}}\times 100\]. Through formula, we have calculated the magnitude and at last % sign is must to show that the required answer is in percentage. Take care while solving decimal numbers.