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A shopkeeper provides successive discounts of 2% and 5%, which are equivalent to a single discount of ____.
7%
7.1%
6.9%
6%
6.9%
Use the formula (d1 + d2) - (d1 × d2 / 100). Here, 2 + 5 = 7, and (2 × 5) / 100 = 10 / 100 = 0.1. So, 7 - 0.1 = 6.9%.
Two successive discounts are provided: 2% and 5%.
Single Discount=(d1+d2)−100d1×d2
Use the formula (d1 + d2) - (d1 × d2 / 100). Here, 2 + 5 = 7, and (2 × 5) / 100 = 10 / 100 = 0.1. So, 7 - 0.1 = 6.9%.
Many students wrongly assume the answer is simply 2% + 5% = 7%, ignoring the fact that the second discount applies to the remaining value after the first discount.
Define the discounts
Identify the two given successive discounts as d1=2% and d2=5%.
d1=2,d2=5
Apply the successive discount formula
The formula for a single equivalent discount is Deq=(d1+d2)−100d1×d2.
Deq=(2+5)−1002×5
Calculate the result
Perform the arithmetic: 2+5=7 and 10010=0.1. Subtracting gives 7−0.1=6.9.
Deq=7−0.1=6.9%
C is correct because the successive application of 2% and 5% discounts results in a net discount of 6.9%.
This concept is identical to the 'successive percentage increase/decrease' formula used in compound interest and population growth problems.
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