Question

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

Answer 1

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}
$
So, The correct option of this question will be (B).

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Trick : Decrease in consumption
$
\begin{array}{l}
=\left(\frac{20}{100+20}\right) \times 100 \\
=16 \frac{2}{3} \% ; \text { Ans. }
\end{array}
$