Percentage Question Answers

Percentages, Ratio Sample Question - CAT 2007

Question 4 the day: March 20, 2006
The question for the day is a sample practice problem in percentages, an Arithmetic Topic.

Question:
If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
 

1. 10%
2. 12%
3. 8%
4. 6.67%

Correct Answer - 8%. Choice (3)
 

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Explanatory Answer

Let the price of 1 litre of petrol be Rs.x and let Raj initially buy 'y' litres of petrol.
Therefore, he would have spent Rs. xy on petrol.

When the price of petrol increases by 25%, the new price per litre of petrol is 1.25x.

Raj intends to increase the amount he spends on petrol by 15%.
i.e., he is willing to spend xy + 15% of xy = 1.15xy

Let the new quantity of petrol that he can get be 'q'.
Then, 1.25x * q = 1.15xy
Or q = (1.15xy/1.25x)=(1.15y)/1.25 = 0.92y.

As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier.
Or a reduction of 8%.