Percentages - Quant/Math - CAT 2010
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)
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 =  0.8 litres.
He has cut down his petrol consumption by 0.2 litres =  = 20% reduction.
There is a short cut for solving this problem.
If the price of petrol has increased by 25%, it has gone up  of its earlier price.
Therefore, the % of reduction in petrol that will maintain the amount of money spent on petrol constant =  =  = 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.
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