| In the new budget, the price of kerosene oil rose by 25%. By how much per cent must a person reduce his consumption of kerosene oil, so that his expenditure on it does not increase? |
A) 20%
B) 25%
C) 50%
D) 40%
Correct Answer: A
Solution :
| Let price of kerosene oil be Rs. x per litre |
| and consumption be y L |
| Then, total expenditure on oil = Rs. x y |
| Now, new price \[=x+\frac{25}{100}\times x\] |
| \[=x+\frac{x}{4}=\frac{5x}{4}\] |
| According to the question, |
| \[xy=\frac{5x}{4}\left( y-\frac{ay}{100} \right)\] |
| \[\Rightarrow \] \[xy=\frac{5x}{4}y\left( 1-\frac{a}{100} \right)\] |
| \[\Rightarrow \] \[\frac{4}{5}=1-\frac{a}{100}\]\[\Rightarrow \]\[\frac{a}{100}=\frac{1}{5}\] |
| \[\Rightarrow \] \[a=20\]% |
| Alternate Method |
| Reduction in consumption \[=\left( \frac{a}{100+a}\times 100 \right)\]% |
| \[=\,\left( \frac{25}{125}\,100 \right)\]%= 20% |
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