Question : A number is decreased by 20% to get another number. The number so obtained is increased by 200% to get a third number. The difference between the third number and the original number is what percentage more or less than the difference between the second and the third number?
Option 1: 15.7% more
Option 2: 15.7% less
Option 3: 12.5% more
Option 4: 12.5% less
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Correct Answer: 12.5% less
Solution : Let the first number be 100 After a 20% decrease, the second number = 100 – 20 = 80 After a 200% increase in the second number, the third number = 80 + $\frac{200}{100}\times 80$ = 240 Difference between the third number and the original number = 240 – 100 = 140 Difference of second and the third number = 240 – 80 = 160 Required percentage = $\frac{160-140}{160}\times 100$ = 12.5% So, the difference between the third number and the original number is 12.5% less than the difference between the second and the third number. Hence, the correct answer is 12.5% less.
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