Percentage Question Answers

Percentages - Quant/Math - CAT 2007

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Question 4 the day:

June 13, 2002

The question for the day is from the topic Percentages.

Question:

If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?

(1) 25%
(2) 16.67%
(3) 20%
(4) 33.33%

Correct Answer - (3)

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Solution:

Let the price of petrol be Rs.100 per litre. Let the user use 1 litre of petrol. Therefore, his expense on petrol = 100 * 1 = Rs.100

Now, the price of petrol increases by 25%. Therefore, the new price of petrol = Rs.125.

As he has to maintain his expenditure on petrol constant, he will be spending only Rs.100 on petrol.
Let �x� be the number of litres of petrol he will use at the new price.

Therefore, 125*x = 100 => x = 100/125=4/5 =0.8 litres.
He has cut down his petrol consumption by 0.2 litres = (0.2/1)*100 = 20% reduction.

There is a short cut for solving this problem.

If the price of petrol has increased by 25%, it has gone up 1/4th of its earlier price.
Therefore, the % of reduction in petrol that will maintain the amount of money spent on petrol constant = 1/(4+1) = 1/5 = 20%

i.e. Express the percentage as a fraction. Then add the numerator of the fraction to the denominator to obtain a new fraction. Convert it to percentage - that is the answer.