The price of onions has been increased by 50 | vedclass

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(B) Let the initial price of onions be $P$ and initial consumption be $C$. Initial expenditure $= P 	imes C$. New price $= P + 0.50P = 1.50P$. Let th

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Let the initial price of onions be $P$ and initial consumption be $C$. Initial expenditure $= P 	imes C$. New price $= P + 0.50P = 1.50P$. Let the new consumption be $C'$. Since the expenditure remains the same: $1.50P 	imes C' = P 	imes C$. $C' = \frac{P 	imes C}{1.50P} = \frac{C}{1.5} = \frac{2}{3}C$. Reduction in consumption $= C - \frac{2}{3}C = \frac{1}{3}C$. Percentage reduction $= (\frac{1/3C}{C}) 	imes 100 = 33 \frac{1}{3} \%$. Alternatively,using the formula: $	ext{Required reduction } \% = \frac{x}{100+x} 	imes 100 = \frac{50}{100+50} 	imes 100 = \frac{50}{150} 	imes 100 = 33 \frac{1}{3} \%$.

The price of onions has been increased by $50 \%$. In order to keep the expenditure on onions the same,the percentage of reduction in consumption has to be:

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