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Triveni's salary was first decreased by 16% and subsequently increased by 25%. The net percentage change in her salary was:
10% increase
10% decrease
5% decrease
5% increase
5% increase
Use the formula x+y+(x├Чy)/100, where x=тИТ16 and y=+25. Thus, тИТ16+25+(тИТ16├Ч25)/100=9тИТ4=5.
Initial salary decrease of 16% followed by a subsequent increase of 25%.
Net┬аPercentage┬аChange=(x+y+100x├ЧyтАЛ)%
Use the formula x+y+(x├Чy)/100, where x=тИТ16 and y=+25. Thus, тИТ16+25+(тИТ16├Ч25)/100=9тИТ4=5.
Students often wrongly calculate it as 25тИТ16=9%, ignoring the multiplicative effect of successive percentage changes on the base value.
Identify percentage changes
Let the initial percentage decrease be x=тИТ16% and the subsequent percentage increase be y=+25%.
x=тИТ16,y=+25
Apply Successive Change Formula
The formula for net percentage change is given by adding the percentages and their product divided by 100.
Netchange=тИТ16+25+100тИТ16├Ч25тАЛ
Calculate the result
Simplifying the equation: тИТ16+25=9 and (тИТ16├Ч25)/100=тИТ400/100=тИТ4. Therefore, 9тИТ4=5%.
Netchange=9тИТ4=5%
D is correct because the net percentage change calculation results in a 5% increase.
This concept is fundamentally linked to Compound Interest calculations where interest is applied successively over multiple periods.
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