Question

The price of an air conditioner was reduced from Rs. 27,000 to Rs. 24,000. Find the rate of discount.

Answer 1

Hint:
Here, we will first find the amount of discount, which is the difference of the new price from an actual price of the given item and then find the rate of discount using the formula, \[{\text{Rate of discount = }}\dfrac{{{\text{Amount of discount}}}}{{{\text{C.P.}}}} \times 100\], where C.P. is the cost price of an item. Then make sure that the required value is in decimal form.

Complete step by step solution:
We are given that the actual price of an air conditioner is Rs. 27,000 and the new price of an air conditioner are Rs. 24,000.
We know that the amount of discount is the difference between the new price from an actual price of the given item.
Subtracting the new price of an air conditioner from the actual price of an air conditioner, we get
\[ \Rightarrow {\text{Rs}}\left( {27000 - 24000} \right) = {\text{Rs. }}3000\]
We also know that the rate of discount is calculated using the formula, that is, \[{\text{Rate of discount = }}\dfrac{{{\text{Amount of discount}}}}{{{\text{C.P.}}}} \times 100\], where C.P. is the cost price of an item.
We are given that the cost price of an air conditioner is the actual price, which is Rs. 27,000.
Substituting the values of the amount of discount and C.P. in the above formula for the rate of discount, we get
\[
  {\text{Rate of discount}} = \dfrac{{3000}}{{27000}} \times 100 \\
   = \dfrac{1}{9} \times 100 \\
   = \dfrac{{100}}{9}\% \\
 \]
Dividing the above fraction to find the decimal form of rate of discount, we get
\[ \Rightarrow {\text{Rate of discount = }}11.11\% \]

Therefore, the rate of discount on an air conditioner is \[11.11\% \].

Note:
Discount is the amount that is reduced on an object, so we say that the cost price is the addition of the selling price and discount. So students should know that when the price is the difference in the original price and the new price is the amount of discount. Some students take a reduced price as the amount of discount, which is wrong. We will write the fraction in decimals to find the appropriate discount.