Question

The cost of an air cooler has increased from Rs.$2250$ to $2500$. What is the percentage change?

Answer 1

Hint: We are given the initial cost price and the final cost price of the air cooler. First, find the difference in the cost by subtracting the initial cost from the final cost. This will tell us the increase in the cost price. Now use the formula-
$\Rightarrow$ Percentage change=${\displaystyle \frac{\text{Increase in cost}}{\text{Initial cost}}}\times 100$
Put the given values in the formula and solve to find the percentage change.

Complete step-by-step answer:
Given, the initial cost of the air cooler =Rs. $2250$
The final cost of the air cooler =Rs. $2500$
Now, we have to find the percentage change. For this we need to find the increase in the cost.
First, we will find the difference between the initial cost price and the final cost of the air cooler.
This difference tells us the increase in the cost of the air cooler.
So we can write-
$\Rightarrow$ Increase in the cost=Final cost-initial cost=$2500-2250$
On solving, we get-
$\Rightarrow$ Increase in the cost=Rs.$250$
Now to find the percentage change we will use the formula-
$\Rightarrow$ Percentage change=${\displaystyle \frac{\text{Increase in cost}}{\text{Initial cost}}}\times 100$
On putting the given values in the formula, we get-
$\Rightarrow$ Percentage change=${\displaystyle \frac{\text{250}}{\text{2250}}}\times 100$
On simplifying, we get-
$\Rightarrow$ Percentage change=${\displaystyle \frac{25}{225}}\times 10$
On dividing numerator and denominator, we get-
$\Rightarrow$ Percentage change=${\displaystyle \frac{\text{5}}{45}}\times 100$
On again dividing the numerator and denominator, we get-
$\Rightarrow$ Percentage change=${\displaystyle \frac{1}{\text{9}}}\times 100$
On again dividing the numerator and denominator, we get-
$\Rightarrow$ Percentage change=${\displaystyle \frac{100}{9}}=11.11\mathrm{\%}$
Hence the correct answer is $11.11\mathrm{\%}$

Note: Here you can also directly use the formula-
Percentage change=${\displaystyle \frac{\text{Final cost - Initial cost}}{\text{Initial cost}}}\times 100$
On putting the given values, we get-
Percentage change=${\displaystyle \frac{2500-2250}{2250}}\times 100$
On solving, we get-
Percentage change=${\displaystyle \frac{250}{2250}}\times 100$
On solving, we get-
Percentage change=${\displaystyle \frac{5}{45}}\times 100={\displaystyle \frac{1}{9}}\times 100$
On solving, we get-
Percentage change=$11.11\mathrm{\%}$
So we will get the same answer.