Question: 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?
Options:
A) 20%
B) 25%
C) 50%
D) 40%
Show Answer
Answer:
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}( y-\frac{ay}{100} ) $
$ \Rightarrow $ $ xy=\frac{5x}{4}y( 1-\frac{a}{100} ) $
$ \Rightarrow $ $ \frac{4}{5}=1-\frac{a}{100} $
$ \Rightarrow $ $ \frac{a}{100}=\frac{1}{5} $
$ \Rightarrow $ $ a=20 $ %
Alternate Method
Reduction in consumption $ =( \frac{a}{100+a}\times 100 ) $ %
$ =,( \frac{25}{125},100 ) $ %= 20%