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A shopkeeper marks his goods 40% above the cost price and allows a discount of 10%. What is his net gain percentage?
24%
26%
28%
30%
26%
Use the net percentage change formula x+y+100xyтАЛ, where markup x=40 and discount y=тИТ10.
Markup percentage = 40%, Discount percentage = 10%.
Net┬аGain%=x+y+100x├ЧyтАЛ
Use the net percentage change formula x+y+100xyтАЛ, where markup x=40 and discount y=тИТ10.
Many students subtract the discount directly from the markup (40тИТ10=30), ignoring the fact that the discount is calculated on the marked price, not the cost price.
Define variables
Let markup be x=40% and discount be y=тИТ10%.
x=40,y=тИТ10
Apply successive percentage formula
Substitute the values into the formula: NetGain%=40+(тИТ10)+10040├Ч(тИТ10)тАЛ.
Net┬аGain%=40тИТ10тИТ100400тАЛ
Final calculation
Simplify the expression to find the final percentage gain.
30тИТ4=26%
B is correct because the application of the successive percentage change formula results in a net gain of 26%.
This formula is identical to the one used for calculating the net change in area when length and breadth of a rectangle are modified, or for consecutive tax/interest applications.
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