The price of sugar is increased by 22 % . A person wants to increase his expenditure by 12% only. By what percent should he decrease his consumption, nearest to one decimal place?

Let the initial price of 1kg sugar is $$=x$$Rs.

As per the question, the price of the sugar is increased by $$22\%$$
Hence, new price of 1kg sugar $$=\dfrac{122 x}{100}=1.22x$$ Rs.

Initial expenditure of the person is $$=x$$Rs.

As per the condition, person increased his expenditure by $$=12%$$

Hence, the new expenditure amount of the person $$=\dfrac{112 x}{100}=1.22x$$Rs.

Hence, the required percentage$$=\dfrac{1.22x-1.12x}{1.22x}\times 100$$
$$\Rightarrow \dfrac{0.1x}{1.22x}\times 100 =8.2\%$$
So the consumption should be decreased by $$8.2\%$$