The price of sugar has been increased by 50%. By how much percent can the consumption of the sugar be decreased in order to keep the expenditure on sugar the same.

Lets take the price of sugar to be ₹ 100 and consumption be 1 kg.

Hence, total expenditure will be

100 x 1 = 100 ……….(1)

The price of sugar is increased by 50%. Hence,

New Price = $100 + 50$% x 100

= $100 + \dfrac{50}{100} \times 100$

= $100 + \dfrac{50}{\cancel{100}} \times \cancel{100}$

= 100 + 50

= ₹ 150

Let's take new consumption to be $x$ kg.

New expenditure = ₹ (150 x $x$)

Given that expenditure should remain same,

$\therefore 150x = 100 \\[1em] \Rightarrow x = \dfrac{100}{150} \\[1em] \Rightarrow x = \dfrac{2}{3}$

Percentage decrease in consumption = $\dfrac{\text{Old Value - New Value}}{\text{Old Value}} \times 100\%$

$= \dfrac{1 - \dfrac{2}{3}}{1} \times 100\% \\[1em] = \dfrac{3 - 2}{3} \times 100\% \\[1em] = \dfrac{1}{3} \times 100\% \\[1em] = \dfrac{100}{3} \% \\[1em] = 33\dfrac{1}{3}\%$

Hence, consumption should be decreased by $33\dfrac{1}{3}$%.