RAS question
A number is first increased by 20%, then by 25%, and finally decreased by 10%. The net percentage change is:
Correct answer: (C) 35%.
A number increased successively by 20% and 25% and then decreased by 10% has a net increase of 35%.
Explanation
NCERT frames percentage as a way of comparing quantities, with percent meaning per hundred. For successive percentage changes, the base changes after each step, so the percentages cannot be treated as separate additions and subtractions on the original number. Take the original number as 100. A 20% increase makes it 120. The next 25% increase is applied to 120, giving 120 x 1.25 = 150. The final 10% decrease is applied to 150, not to the original 100, so the value becomes 150 x 0.90 = 135. The final value is 35 more than the starting value of 100; therefore, the net percentage change is a 35% increase.
Why the other options are wrong
- (A) 30% understates the gain because the two increases first take 100 to 150, and even after a 10% decrease from 150 the value remains 135.
- (B) 40% would come from reducing 150 by only 10 points of the original number, but the 10% decrease must be calculated on 150.
- (D) 45% leaves too much of the earlier gain intact; the final 10% decrease cuts 15 from 150, bringing the final value down to 135.
Concept
This tests successive percentage change under comparing quantities. It recurs in RAS mental ability because candidates must track the changing base rather than add percentage figures mechanically.