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David's salary was first decreased by 40% and subsequently increased by 50%. What percentage did he lose from his initial salary?
14%
10%
15%
12%
10%
Use the successvie percentage change formula: тИТ40+50+100(тИТ40├Ч50)тАЛ=10тИТ20=тИТ10%
Initial salary of David is decreased by 40% and then increased by 50%.
Net%Change=(100x├ЧyтАЛ)+x+y
Use the successvie percentage change formula: тИТ40+50+100(тИТ40├Ч50)тАЛ=10тИТ20=тИТ10%
Many students mistakenly add or subtract the percentages directly (50тИТ40=10% increase) or calculate the 50% increase on the original salary rather than the decreased amount.
Assume Initial Salary
Let David's initial salary be 100.
Initial=100
Calculate After Decrease
A 40% decrease reduces the salary to 100тИТ(0.40├Ч100)=60.
60
Calculate After Increase
A 50% increase on the new salary of 60 is 60+(0.50├Ч60)=60+30=90.
90
Find Final Percentage Loss
The change from the initial 100 to the final 90 is a loss of 100тИТ90=10. This is a 10% loss on the initial amount.
Loss%=100100тИТ90тАЛ├Ч100=10%
B is correct because the final salary is 90% of the initial, resulting in a 10% loss.
This successive change method is identical to calculating Compound Interest over two periods or successful price discounts, and applies to any area-based changes (e.g., rectangle length/breadth).
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