The price of a commodity has been increased by 60%. By what per cent m

1.	The price of a commodity has been increased by 60%. By what per cent must a consumer reduce the consumption of the commodity so as not to increase his expenditure on the commodity (a) 30% (b) 35% (c) 27.5% (d) 37.5%
Answer» (d) 37.5% Let the price of the commodity be Rs x and its consumption be y. Then Expenditure = Rs xy Increased price = Rs \(\frac{160}{100}\)x = Rs 1.6x Expenditure remaining the same = Rs xy \(\therefore\) Reduced consumption = \(\frac{Xy}{1.6X}\) = \(\frac{10y}{16}\) = \(\frac{5}{8}\)y % reduction in consumption = \(\frac{y-\frac{5}{8}y}{y}\)x 100 = \(\frac{3}{8}\)x 100% = 37.5%

The price of a commodity has been increased by 60%. By what per cent must a consumer reduce the consumption of the commodity so as not to increase his expenditure on the commodity (a) 30% (b) 35% (c) 27.5% (d) 37.5%

Answer»

(d) 37.5%

Let the price of the commodity be Rs x and its consumption be y. Then

Expenditure = Rs xy

Increased price = Rs \(\frac{160}{100}\)x = Rs 1.6x

Expenditure remaining the same = Rs xy

\(\therefore\) Reduced consumption = \(\frac{Xy}{1.6X}\) = \(\frac{10y}{16}\) = \(\frac{5}{8}\)y

% reduction in consumption = \(\frac{y-\frac{5}{8}y}{y}\)x 100

= \(\frac{3}{8}\)x 100% = 37.5%