The price of rice has been increased by 20 %. | vedclass

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Question

(B) Let the original price of rice be $100$ units and the original consumption be $100$ units.Original expenditure $= 100 	imes 100 = 10000$ units.Af

Vedclass · Accepted Answer

$16 \frac{2}{3} \%$

Vedclass · Answer

(B) Let the original price of rice be $100$ units and the original consumption be $100$ units.Original expenditure $= 100 	imes 100 = 10000$ units.After a $20 \%$ increase,the new price of rice is $120$ units.To keep the expenditure the same ($10000$ units),let the new consumption be $C$.$120 	imes C = 10000 \implies C = \frac{10000}{120} = \frac{250}{3} = 83.33$ units.Reduction in consumption $= 100 - 83.33 = 16.67$ units.Percentage reduction $= \left( \frac{16.67}{100} 	imes 100 ight) = 16.67 \% = 16 \frac{2}{3} \%$.Alternatively,using the formula: $	ext{Required percentage} = \left( \frac{x}{100+x} 	imes 100 ight) \%$,where $x = 20$.$= \left( \frac{20}{100+20} 	imes 100 ight) = \frac{20}{120} 	imes 100 = \frac{1}{6} 	imes 100 = 16 \frac{2}{3} \%$.

The price of rice has been increased by $20 \%$. By what per cent should Sanjay reduce the consumption of rice in the family so that the expenditure on rice remains the same as before the increase in the price of rice?

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