Percentages - Quant/Math - CAT 2007
Question 4 the day:
May 30, 2002
The question for the day is from the topic Percentages.
Question:
- Peter got 30% of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What was the passing marks in the examination?
(1) 35
(2) 250
(3) 75
(4) 85
Correct Answer - (4)
Solution:
Let ‘x’ be the maximum marks in the examination.
Therefore, Peter got 30% of x =  = 0.3x
And Paul got 40% of x =  = 0.4x.
In terms of the maximum marks Paul got 0.4x - 0.3x = 0.1x more than Peter. —— (1)
The problem however, states that Paul got 15 marks more than the passing mark and Peter got 10 marks less than the passing mark.
Therefore, Paul has got 15 + 10 = 25 marks more than Peter. —— (2)
Equating (1) and (2), we get
0.1x = 25 => x =  = 250
‘x’ is the maximum mark and is equal to 250 marks.
We know that Peter got 30% of the maximum marks. Therefore, Peter got  = 75 marks.
We also know that Peter got 10 marks less than the passing mark. Therefore, the passing mark will be 10 marks more than what Peter got = 75 + 10 = 85.
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