The price of sugar is increased by 20%. By what percent must the consumption of sugar be decreased so that the expenditure on sugar may remain 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 20%. Hence,

New Price = $100 + 20$% x 100

= $100 + \dfrac{20}{100} \times 100$

= $100 + \dfrac{20}{\cancel{100}} \times \cancel{100}$

= 100 + 20

= ₹ 120

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

New expenditure = ₹ (120 x $x$)

Given that expenditure should remain same,

$\therefore 120x = 100 \\[1em] \Rightarrow x = \dfrac{100}{120} \\[1em] \Rightarrow x = \dfrac{5}{6}$

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

$= \dfrac{1 - \dfrac{5}{6}}{1} \times 100\% \\[1em] = \dfrac{6 - 5}{6} \times 100\% \\[1em] = \dfrac{1}{6} \times 100\% \\[1em] = \dfrac{100}{6} \% \\[1em] = \dfrac{50}{3} \% \\[1em] = 16\dfrac{2}{3}\%$

Hence, consumption should be decreased by $16\dfrac{2}{3}$%.