If the sugar price is increased by 25%, by how much per cent should consumption be reduced so that the expense remains the same?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20%
Expense = price × consumption. For the expense to stay the same, consumption must fall in the same ratio as the price rises.
Assuming the old price to be 100 and the old consumption to be 1 unit:
Old expense \(=100\times1=100\)
New price \(=125\), so the consumption that keeps the expense at 100 is \(\displaystyle\frac{100}{125}=0.8\) unit
Reduction \(=1-0.8=0.2\), that is, 20%
Tip: For a price rise of \(r\%\), the cut in consumption is \(\displaystyle\frac{r}{100+r}\times100\%\); here \(\frac{25}{125}\times100=20\%\). It is always less than \(r\%\), because the cut is taken on the higher price.