In a test, X scores 25% of the maximum marks and fails by 40 marks. Y scores 45% of the maximum marks and gets 20 marks more than the pass mark. What are the maximum marks for the test?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 300
Both results fix the same pass mark, so the gap between the two scores, 20%, is worth 40 + 20 marks.
Pass mark \(=25\%\) of M \(+\,40=45\%\) of M \(-\,20\)
\(20\%\) of M \(=40+20=60\)
M \(\displaystyle =\frac{60\times100}{20}=300\)
Check: pass mark \(=75+40=115\)
The maximum marks are 300.
Why the other options are incorrect
Option (2) 100 — Incorrect. With 100 maximum marks, X’s result gives a pass mark of 65 but Y’s gives 25; they must agree.
Option (3) 160 — Incorrect. With 160 maximum marks, X’s result gives a pass mark of 80 but Y’s gives 52; they must agree.
Option (4) 200 — Incorrect. With 200 maximum marks, X’s result gives a pass mark of 90 but Y’s gives 70; they must agree.