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Two successive discounts of 20% and 15% on a deal are equivalent to a single discount of:
35%
32%
30%
33%
32%
Given: Two successive discounts of 20% and 15% are applied to a deal.
Two successive discounts of 20% and 15% are applied to a deal.
DeqтАЛ=x+yтИТ100x├ЧyтАЛ
Use the effective percentage formula: x+yтИТ(xy/100). Here, 20+15тИТ(20├Ч15/100)=35тИТ3=32.
Most students mistakenly add 20% + 15% to get 35%, ignoring that the second discount applies to the remaining 80% of the original value.
Identify Successive Discounts
Let the first discount be x=20% and the second discount be y=15%.
x=20,y=15
Apply Successive Discount Formula
The formula for equivalent single discount is given by DeqтАЛ=x+yтИТ100x├ЧyтАЛ.
DeqтАЛ=20+15тИТ10020├Ч15тАЛ
Calculate the Result
Calculating the values: 20+15=35 and 10020├Ч15тАЛ=3. Subtracting these, we get 35тИТ3=32%.
DeqтАЛ=35тИТ3=32%
B is correct because the calculation of successive discounts results in an equivalent single discount of 32%.
This formula is identical to the one used for compound percentage increases (like population growth or compound interest over two periods: x+y+100xyтАЛ), but with a negative sign for discounts.