The price of sugar increases by 15%. By what percentage should the consumption of sugar be decreased so that the expenditure on the purchase of sugar remains the same? [Give your answer correct to 2 decimal places.]

Let's assume the price and consumption of sugar initially is 10z and 10y respectively.

Total expenditure = $$10z\times10y$$ = 100yz

The price of sugar increases by 15%.

Price of sugar after increase = 10z of (100+15)%

= 10z of 115%

= $$10z\times\frac{115}{100}$$

= 11.5z

As per the information given in the question, the price of sugar increased but expenditure should not be changed. It means that consumption should be decreased.

 consumption of sugar after price increase = $$\frac{100yz}{11.5z}$$ = $$\frac{1000y}{115}$$ = $$\frac{200y}{23}$$

Percentage decrease in the consumption of sugar = $$\frac{10y-\frac{200y}{23}}{10y}\times\ 100$$

= $$\frac{\frac{230y-200y}{23}}{10y}\times\ 100$$

= $$\frac{30y}{230y}\times\ 100$$

= $$\frac{300}{23}$$

= 13.04% (approx.)