Question : A number is first increased by 16% and then increased by 20%. The number so obtained has now decreased by 40%. The net decrease percentage in the original number is:
Option 1: $16 \frac{12}{25}$%
Option 2: $15 \frac{9}{25}$%
Option 3: $11 \frac{13}{25}$%
Option 4: $13 \frac{7}{25}$%
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Correct Answer: $16 \frac{12}{25}$%
Solution :
Let the number be $100x$.
First increase = 16%
Second increase = 20%
Third decrease = 40%
Resultant number = $100x × \frac{100+16}{100} × \frac{100+20}{100} × \frac{100-40}{100}$ = $\frac{2088}{25}x$
Percentage decrease = $\frac{100x - \frac{2088}{25}x}{100x}×100$ = $\frac{412}{25}$ = $16\frac{12}{25}$%
Hence, the correct answer is $16\frac{12}{25}$%.
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