Question

The list price of a watch is Rs. 400. A customer gets two successive discounts, the first being 10%. Calculate in percentage, the second discount, if the customer pays Rs. 306 for it.

Answer 1

Hint- Use the formula of discount percentage and find out the discounts. For two successive discounts find the money to be paid after the first discount and thereafter apply the second discount on the modified cost price for the customer.

Compete step-by-step solution -
Given that the marked price of the watch is Rs. 400 and first discount percent is 10%.
Discount applied on the watch after first discount is:
10% of the marked price.
$
   = 10\% {\text{ }}of{\text{ }}Rs.400 \\
   = \dfrac{{10}}{{100}} \times Rs.400 \\
   = Rs.40 \\
 $
So the price of the watch after first discount is:
$
   = {\text{marked price}} - {\text{discount}} \\
   = Rs.400 - Rs.40 \\
   = Rs360 \\
 $
Let the second discount given on the watch be $x\% $
So discount applied on the watch after second discount is:
$x\% $ of the first discounted price.
$
   = x\% {\text{ }}of{\text{ }}Rs.360 \\
   = \dfrac{x}{{100}} \times Rs.360 \\
   = Rs.\dfrac{{360x}}{{100}} \\
 $
So the price of the watch after second discount is:
$
   = {\text{first discounted price}} - {\text{second discount}} \\
   = Rs.360 - Rs.\dfrac{{360x}}{{100}} \\
   = Rs\dfrac{{36000 - 360x}}{{100}} \\
 $
Also this value is given in the question i.e. Rs.306 so comparing :
\[
   \Rightarrow Rs\dfrac{{36000 - 360x}}{{100}} = Rs.306 \\
   \Rightarrow \dfrac{{3600 - 36x}}{{10}} = 306 \\
   \Rightarrow 3600 - 36x = 3060 \\
   \Rightarrow 36x = 3600 - 3060 \\
   \Rightarrow 36x = 540 \\
   \Rightarrow x = \dfrac{{540}}{{36}} = 15 \\
 \]
Hence, the second discount is 15%.

Note- In order to solve such a question, a common mistake done is addition of two discount percentages. Never add the discount percentage directly till it is not mentioned specifically in the question that may lead to false results. Always separately find out both of the discounts one by one as done above. This question could also have been solved by directly finding the selling price by subtracting the discount percentage from 100 and multiplying by cost price.