Question

The price of the car was Rs. 3 lakh fifty thousand and after three years its price goes up to Rs. 3 lakh eighty thousand, find the percentage increase in the price?

Answer 1

Hint:
 We start solving the problem by assigning variables to the new and old prices of the car. We then write the new and old prices in terms of numbers using the given price in words. We then recall the fact that the percentage increase in the price of car as $ \%p=\dfrac{\text{New price}-\text{Old price}}{\text{Old price}}\times 100 $ and then substitute the value in it. We then make the necessary calculations to get the required percentage of increase in the price of a car.

Complete step by step answer:
According to the problem, we are given that the price of the car was Rs. 3 lakh fifty thousand and after three years its price goes up to Rs. 3 lakh eighty thousand. We need to find the percentage increase in the price of the car.
Let us assume the old price and new price as $ {{p}_{1}} $ and $ {{p}_{2}} $ .
So, we have $ {{p}_{1}}=Rs.3,50,000 $ and $ {{p}_{2}}=Rs.3,80,000 $ .
We know that the percentage increase in the price of car is defined as $ \%p=\dfrac{\text{New price}\left( {{p}_{2}} \right)-\text{Old price}\left( {{p}_{1}} \right)}{\text{Old price}\left( {{p}_{1}} \right)}\times 100 $ .
 $ \Rightarrow \%p=\left( \dfrac{3,80,000-3,50,000}{3,50,000} \right)\times 100 $ .
 $ \Rightarrow \%p=\left( \dfrac{30,000}{3,50,000} \right)\times 100 $ .
 $ \Rightarrow \%p=\left( \dfrac{3}{35} \right)\times 100 $ .
 $ \Rightarrow \%p=8.57\% $ .
 $\therefore$ We have found the percentage increase in the price of the car at 8.57%.

Note:
We should remember that the percentage increase in price will be calculated w.r.t old price while solving this type of problem. We should not multiply with 100 if it is not mentioned to provide the answer in percentage. Similarly, we can expect problems to find the profit on selling the car at Rs. 4 lakh 20 thousand after 3 years.