Question

If the price of coal be raised by $20$% find by how much percent a housewife must reduce her consumption of that article so as not to increase her expenditure.

• A. $40$%
• B. $16\frac{2}{3}$%
• C. $10$%
• D. $33\frac{1}{3}$%

Answer 1

The correct option is B $16\frac{2}{3}$%

The increase in price is $20\%$

Let the price of $1$ unit be $x$ initially.

The increased price is $[1+\frac{1}{5}]x=\frac{6}{5}x$

The multiplication factor for $\frac{6}{5}x$ to make it $x$ is $\frac{5}{6}$

The Percentage to be decreased iin the comsumption is $20\times \frac{5}{6}$

$⟹\frac{50}{3}\%$

$⟹16\frac{2}{3}\%$