The price of sugar is increased by 24%. A person wants to increase his expenditure by 15% only. By what percentage, correct to one decimal place, should he reduce his consumption?

Let the initial price of the sugar is Rs. x and the expenditure is also Rs. x.

When the rate of sugar is increased by $$24\%$$

So, new rate of the sugar $$=\dfrac{124x}{100} =1.24x$$

Increase in expenditure$$=15\%$$

So, new expenditure $$=\dfrac{115x}{100}=1.15x$$

Hence, the required percentage $$=\dfrac{(1.24x - 1.15x)\times 100}{1.24x}=\dfrac{0.09\times 100}{1.24}$$

$$\Rightarrow$$percentage of reduction in consumption$$ =7.3 \%$$