The price of sugar is decreased by 20%. By what percentage should a family increase its consumption so that its expenditure on sugar remains the same?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 25%
Expenditure \(=\) price \(\times\) consumption. Take the old price and consumption as 100 each; the new consumption must bring the product back to the same value.
New price \(=100-20=80\)
Consumption needed \(\displaystyle =\frac{100\times100}{80}=125\)
Increase \(=125-100=25\), that is 25%
The consumption must rise by 25%.
Why the other options are incorrect
Option (1) 40% — Incorrect. With a rise of 40%, spending becomes \(0.8\times1.4=1.12\) of the old spending, not the same.
Option (3) \(16\frac{2}{3}\%\) — Incorrect. This is the change needed when the price rises; here it falls.
Option (4) 20% — Incorrect. Raising consumption by 20% does not make up for a 20% price fall: \(0.8\times1.2=0.96\), less than 1.