The price of cooking gas has increased by 25%. By what percent should a family reduce the use of cooking gas so as not to increase the expenditure on this account?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20%
Expenditure is price × quantity. To keep it the same after a price rise, the quantity must fall in proportion to the new price, so the cut is worked out on the new price, not the old one.
Assuming the old price to be 100:
New price \(=125\)
Cut needed \(\displaystyle =\frac{125-100}{125}\times100=\frac{25}{125}\times100=20\%\)
Tip: For a price rise of \(r\%\), the cut in use is \(\displaystyle \frac{r}{100+r}\times100\) per cent; it is always smaller than \(r\), which is why 25% is not the answer.