If the price of sugar be increased by $20 \%$, then find by how much percent must its consumption be decreased to keep the expenditure fxed on sugar.
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If the price of sugar be increased by $20 \%$, then find by how much percent must its consumption be decreased to keep the expenditure fxed on sugar.

(a) $20 \%$

(b) $16 \frac{2}{3} \%$

(c) $25 \%$

(d) $33 \frac{1}{3} \%$
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Solution

 Let the initial price of sugar $=$ Rs. 100 per $\mathrm{kg}$.

New price $=100+20$

$=$ Rs. 120 per kg.

$\because$ For Rs. 120 , we get $1 \mathrm{~kg}$ of sugar.

$\therefore$ For Re. 1 we get $\frac{1}{120} \mathrm{~kg}$ of sugar.

$\therefore \quad$ For Rs. 100 we get $\frac{1}{120} \times 100$

$$

=\frac{5}{6} \mathrm{~kg}

$$

$$

\text { Reduction }=1-\frac{5}{6}=\frac{1}{6} \mathrm{~kg}

$$

$$

\begin{aligned}

\therefore \quad \text { Decrease in\% } &=\frac{\frac{1}{6} \mathrm{~kg}}{1 \mathrm{~kg}} \times 100 \\

&=\frac{1}{6} \times \frac{1}{1} \times 100 \\

&=\frac{50}{3} \\

&=16 \frac{2}{3} \% ; \text { Ans. }

\end{aligned}

$$

$\therefore \quad$ True option $=(b)$



Trick : Decrease in consumption

$$

\begin{array}{l}

=\left(\frac{20}{100+20}\right) \times 100 \\

=16 \frac{2}{3} \% ; \text { Ans. }

\end{array}

$$

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