| Price of a commodity has increased by 60%. By what per cent must a consumer reduce the consumption of the commodity, so as not to increase the expenditure? [SSC (CGL) 2011] |
A) 37
B) 37.5
C) 40.5
D) 60
Correct Answer: B
Solution :
| (b) Let the reduction in consumption be\[x\]% |
| Then, \[60-x-\frac{60x}{100}=0\] |
| \[\Rightarrow \] \[60-x-\frac{3x}{5}=0\] \[\Rightarrow \] \[300-5x-3x=0\] \[\Rightarrow \] \[8x=300\] |
| \[\therefore \text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }\!\!~\!\!\text{ }x=\frac{300}{8}=37.5\] % |
| Alternate Method |
| If the price of a commodity increases or decreases by a%. Then, the decrease or increase in consumption, so as not to increase or decrease the expenditure is equal to \[\left( \frac{a}{100\pm a} \right)\times 100\]% |
| Here, \[a=60\] |
| Then, deduction percentage=\[\frac{60}{160}\times 100=\frac{600}{16}=37.5\]% |
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