Question

# A single discount to two successive discounts of 20% and 5% is _________________%.

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Hint:Discount refers to the condition of the price of a bond that is lower than the face value. The discount equals the difference between the price paid for and it’s par value.
Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.
Successive Discount : The formula for total discount in case of successive-discounts :
If the first discount is x% and 2nd discount is y% then ,
Total discount = $x + y - \left( {\dfrac{{{\text{ }}xy}}{{100}}{\text{ }}} \right){\text{ }}\%$…………………………………..(1)

Method 1:-
Let the marked price =Rs 100
First discount x = 20%
Second discount y = 5%
So applying formula (1) mentioned in hint
Total discount = $20 + 5 - \left( {\dfrac{{{\text{ }}\left( {20} \right)\left( 5 \right)}}{{100}}{\text{ }}} \right){\text{ }}\%$
$= 25 - \left( {\dfrac{{{\text{ 100}}}}{{100}}{\text{ }}} \right){\text{ }}\% \\ = 25 - 1 \\ = 24 \\$
Method 2:-
First discount x = 20%
Price to be paid is = 0.80 of market price
Second discount y = 5% = 0.95
Price to be paid is = 0.95 of market price
So, total discount = $1 - \left( {0.80{\rm X}0.95} \right) = 0.24 = 24\%$
A single discount to two successive discounts of 20% and 5% is 24%.

Note:The most important question is which discount is better among Successive discount and One Time Discount. So here by means of an example, we will explain the simple tricks to solve these Successive Discount based question quickly
Case 1: Successive discount 10% and then 20%, Final price you’ve to pay = 0.90 x 0.80 x original price = 0.72 x original price
Case 2: Discount offered=29%, Final price you’ve to pay = 0.71 times original price, which is less than Case 1, means it is a better deal.