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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) $33 \frac{1}{3} \%$

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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