Question

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 ?

Answer 1

Let price of x kg of sugar = Rs. 100
Increase in price = 20%
$\therefore$ New price = 100 +20 = Rs. 120
$\therefore$ For Rs.. 120, sugar obtained = x kg.
For Rs. 100, sugar obtained = $\frac{x}{120}\times 100=\frac{5x}{6}$ kg
Original consumption = $\frac{5x}{6}$ kg
Decrease in comsuption = $x-\frac{5x}{6}=\frac{x}{6}$
Required % of decrease in consumption
= $\frac{\frac{x}{6}}{x}\times 100=\frac{x}{6x}\times 100=\frac{100}{6}=\frac{50}{3}=16\frac{2}{3}$ %