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
Solution:
Let �x� be the maximum marks in the examination.
Therefore, Peter got 30% of x = (30/100)x = 0.3x
And Paul got 40% of x = (40/100)*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 = 25/0.1= 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 (30/100)*250 = 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.
