In an examination 35% of the student passed and 455 students failed. How many students appeared for the examination.

The correct answer is B.

Since 35% passed, the failed share must be 100 − 35 = 65% of the total. Let the total be T. Then 0.65T = 455, so T = 455 ÷ 0.65 = 700. Check: 65% of 700 is 455 failed, and 35% of 700 is 245 passed, which together make 700.

• A) 490: 65% of 490 is 318.5, not 455, so the failure count does not match.
• C) 845: 65% of 845 is 549.25, far from 455.
• D) 1300: This comes from dividing 455 by 35 (455 ÷ 0.35 = 1300), which wrongly treats 455 as the 35% who failed. The failure figure must be matched with the 65% failure share.

The core concept is percentage as a part of a whole, with the complement rule: if x% pass, then (100 − x)% fail. This is basic arithmetic that recurs in Prelims quantitative and data-interpretation questions, and the same proportional reasoning helps in reading statistics in Mains answers on education and governance.

Trap: Dividing by 35 because the passing percentage is mentioned first, instead of using the failure percentage of 65.