Question

A car is marked at Rs.300000. The dealer allows successive discounts of 6%, 4% and $2\dfrac{1}{2}\%$ on it. What is the net selling price?
\[\begin{align}
  & A.Rs.253852 \\
 & B.Rs.283462 \\
 & C.Rs.241962 \\
 & D.Rs.263952 \\
\end{align}\]

Answer 1

Hint: In this question, we are given the market price of a car on which successive discounts are given as 6%, 4% and $2\dfrac{1}{2}\%$. We need to find a net selling price. For this, we will first find a discount on the price after applying a 6% discount on the original price. Then we will find the next discounted price after applying a 4% discount on the previous discount price (discount price after 6%). At last, we will find the discounted price after applying $2\dfrac{1}{2}\%$ discount on the previous discount price (discount price after 4%). The discount price is given by $P\left( 1-\dfrac{d}{100} \right)$ where P is the amount on which discount is applied and d is the discount percentage.

Complete step-by-step solution
Here we are given the actual price of the car as Rs.300000.
Successive discounts of 6%, 4%, and $2\dfrac{1}{2}\%$ are given on the price of the car. We need to find the net selling price.
The First 6% discount is given at the actual price of the car. As we know, the discount price is given by $\text{Discounted price}=P\left( 1-\dfrac{d}{100} \right)$.
Where P is the amount on which discount is applicable and d is the discount percentage.
So after applying a 6% discount on Rs.300000 we get a discounted price as,
Discounted price after 6% discount \[\Rightarrow 300000\left( 1-\dfrac{6}{100} \right)\].
Taking LCM in bracket we get:
\[\begin{align}
  & \Rightarrow 300000\left( \dfrac{100-6}{100} \right) \\
 & \Rightarrow 300000\times \dfrac{94}{100} \\
 & \Rightarrow 3000\times 94 \\
 & \Rightarrow Rs.282000 \\
\end{align}\]
After 6% discount price of car reduces to Rs.282000.
Now 4% discount is given at previous discounted price i.e. 4% discount is given at Rs.282000
Hence, discounted price after 4% discount becomes equal to,
\[\begin{align}
  & \Rightarrow 282000\left( 1-\dfrac{4}{100} \right) \\
 & \Rightarrow 282000\left( \dfrac{100-4}{100} \right) \\
 & \Rightarrow 282000\times \dfrac{96}{100} \\
 & \Rightarrow 2820\times 96 \\
 & \Rightarrow Rs.270720 \\
\end{align}\]
Hence after an additional 4% discount, the price of car reduces to Rs.270720.
Again $2\dfrac{1}{2}\%$ discount is given at the previous discounted price i.e. $2\dfrac{1}{2}\%$ discount is given at Rs.270720.
$2\dfrac{1}{2}\%$ can be written as $\dfrac{5}{2}\%$. So,
Discounted price after $\dfrac{5}{2}\%$ discount becomes equal to,
\[\begin{align}
  & \Rightarrow 270720\left( 1-\dfrac{\dfrac{5}{2}}{100} \right) \\
 & \Rightarrow 270720\left( 1-\dfrac{5}{200} \right) \\
 & \Rightarrow 270720\left( \dfrac{200-5}{200} \right) \\
 & \Rightarrow 270720\times \dfrac{195}{200} \\
 & \Rightarrow \dfrac{52790400}{200} \\
 & \Rightarrow Rs.263952 \\
\end{align}\]
Hence after $2\dfrac{1}{2}\%$ discount, the price of the car reduces to Rs.263952.
So, the net selling price of the car becomes equal to Rs.263952.
Hence, option D is the correct answer.

Note: Students should note that we have to take the previous discount price as P for the next application of discount. Students can make the mistake of calculating discounts on the same amount only. They can also make the mistake of adding all discounts and then applying them to the price of the car. Take care of signs while applying the formula.