Aman got 30% of the maximum marks in an examination and failed by 15 marks. However, Anil who took the same examination got 40% of the total marks and got 10 marks more than the passing marks. What were the passing marks in the examination?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 90
Note: It seems that there is a mistake in the original NTA paper, which prints that Aman “failed by 15% marks”; with 15% the question cannot be solved. To arrive at the NTA answer, it should read “failed by 15 marks”, and it is so shown here, as explained below.
Both students give the same passing mark: Aman’s score plus the 15 marks he fell short by, and Anil’s score minus the 10 marks he had to spare. Setting these equal gives the maximum marks M.
From Aman: passing marks \(=0.30M+15\)
From Anil: passing marks \(=0.40M-10\)
The two expressions are equal: \(0.30M+15=0.40M-10\)
So 10% of the maximum marks is 25: \(0.10M=25\), \(M=250\)
Passing marks \(=0.30\times250+15=75+15=\) 90