A student has to secure 45% of marks to pass an examination. He gets only 50 marks and fails by 4 marks. The maximum marks is

Work from the pass mark first. He scored 50 and failed by 4, so the passing mark is 54, not 46. Subtracting is the first slip most people make. Now find M such that 45% of M = 54, which gives M = 54 × 100 / 45 = 120. Option B is correct.

Check the rest against the same pass mark:

• A (110): 45% of 110 is 49.5. He would pass with 50, so this contradicts the question.
• C (135): 45% of 135 is 60.75. The pass mark would be far above 54, so he would fail by about 10.75.
• D (150): 45% of 150 is 67.5. He would fail by 17.5, not 4.

The core concept is the percentage-to-total relation: pass mark = (pass %) × maximum, so maximum = pass mark ÷ pass %. Such questions come up often in Prelims, and the same reasoning applies to cut-off and normalisation problems.

Trap: Computing 46 ÷ 0.45 (about 102), which is not an option, or forgetting that the pass mark is the score plus the shortfall (50 + 4 = 54).