RAS question
If the price of sugar increases by 25%, by what percentage should a household reduce consumption so that the expenditure remains the same?
Correct answer: (C) 20%.
If the price of sugar rises by 25%, consumption must be reduced by 20% to keep the household's expenditure unchanged.
Explanation
This is a percentage-change problem with expenditure kept constant. NCERT's Comparing Quantities material treats per cent as a way to compare quantities out of 100, so the calculation must be made against the new price, not simply mirrored from the price rise. Let the original price be Rs 100 per kg and the original consumption be 1 kg; the expenditure is Rs 100. After a 25% rise, the price becomes Rs 125. To spend the same Rs 100, the household can buy only 100/125 = 0.8 kg. Consumption has therefore fallen from 1 kg to 0.8 kg, a reduction of 0.2 kg out of 1 kg, which is 20%.
Why the other options are wrong
- (A) A 15% reduction leaves consumption at 85% of the original, so expenditure becomes 125% x 85% = 106.25% of the original expenditure.
- (B) A 25% reduction incorrectly mirrors the price rise; it leaves consumption at 75%, making expenditure 125% x 75% = 93.75% of the original.
- (D) A 30% reduction is too large because 70% consumption at the new price gives only 125% x 70% = 87.5% of the original expenditure.
Concept
This tests percentage change under a constant total, a standard Comparing Quantities idea in the Reasoning and Mental Ability section. It recurs in RAS-style aptitude because price, consumption and expenditure questions check whether the candidate can handle inverse percentage relationships, not just apply a direct percentage.