Question

A washing machine is marked at Rs. 7500. The dealer allows successive discounts of $8\% $, $5\% $ and $2\% $ on it. What is the net selling price?

Answer 1

Hint: The successive discount is just like compound interest that gives interest on interest. Successive discount means offering a discount on a product multiple times one after the other.
Here we have 3 discounts i.e. one after the other. We have to calculate the net price after the first discount and then apply the next discount on the net price obtained from the previous one and so on.

Complete step-by-step answer:
We are given with market price of a washing machine i.e.
 $M.P = Rs.7500$
 Firstly, we have to calculate the net price of the washing machine after first discount of $8\% $ and discount can be calculated i.e.
 $ \Rightarrow {D_1} = 8\% \times 7500$ , where ${D_1}$is the first discount.
  $ \Rightarrow {D_1} = \dfrac{8}{{100}} \times 7500$
By cancelling zeroes in numerator with denominator we get,
 $ \Rightarrow {D_1} = 8 \times 75 = Rs.600$
 For calculate net price after first discount i.e. $N.{P_1}$
$ \Rightarrow N.{P_1} = M.P - {D_1}$
$ \Rightarrow N.{P_1} = 7500 - 600$
$ \Rightarrow N.{P_1} = Rs.6900$
 Now, we will calculate the discount on this net price after the first discount. To calculate the net price of the washing machine after second discount of $5\% $ and discount can be calculated i.e.
$ \Rightarrow {D_2} = 5\% \times 6900$ , where ${D_2}$is the second discount.
  $ \Rightarrow {D_2} = \dfrac{5}{{100}} \times 6900$
By cancelling zeroes in numerator with denominator we get,
$ \Rightarrow {D_2} = 5 \times 69 = Rs.345$
 For calculate net price after 2nd discount i.e. $N.{P_2}$
$ \Rightarrow N.{P_2} = N.{P_1} - {D_2}$
$ \Rightarrow N.{P_2} = 6900 - 345$
$ \Rightarrow N.{P_2} = Rs.6555$
 To calculate net selling price after 3rd discount and discount is given by:
$ \Rightarrow {D_3} = 2\% \times 6555$ , where ${D_3}$is the third discount.
  $ \Rightarrow {D_3} = \dfrac{2}{{100}} \times 6555$
By cancelling numerator with denominator, we get,
$ \Rightarrow {D_3} = Rs.131.1$
 For calculate net selling price after 3rd discount i.e. $S.P$
$ \Rightarrow S.P = N.{P_2} - {D_2}$
$ \Rightarrow S.P = 6555 - 131.1$
$ \Rightarrow S.P = Rs.6423.90$ ……………..(1)
 Hence, net selling price of washing machine is Rs. 6423.90.

Note: Generally, students make mistakes in applying successive discounts, they simply add all the discounts and then subtract it from market price. This is the wrong method. As there is a difference in subtracting discount and successive discount, in this we apply discount on the net price obtained from previous discount.
As $8 + 5 + 2 = 13\% $
While applying this discount on market price we get,
$
   \Rightarrow S.P = 7500 - \dfrac{{13}}{{100}} \times 7500 \\
   \Rightarrow S.P = 7500 - 975 \\
$
$ \Rightarrow S.P = Rs.6525$ …………….(2)
Here you can see the difference in both the value of selling price given in (1) and (2). The value of S.P in (1) is the right one.