R targets to score 85% marks in exams. He scores 450 marks and misses the target by 35%. How much increment in percentage should be there in his scored marks to meet the target?

Correct — C. Missing an 85% target by 35% means R landed 35 percentage points low, so he actually scored 50%.

450 = 50% of the maximum → maximum = 900
Target in marks = 85% of 900 = 765

Shortfall = 765 − 450 = 315
An increment is measured on what he scored: 315⁄450 × 100 = 70% → option (c)

Why the others are wrong

• (a)
  53 — 53 follows the other reading of the stem — 35% of the target rather than 35 percentage points. Then 450 is 65% of the target and the rise needed is 100⁄65 − 1 ≈ 53.8%.
• (b)
  45 — 45 matches no step here. Raising 450 by 45% gives 652.5 marks, still more than a hundred short of the 765 the target needs.
• (d)
  35 — 35 is the miss restated, not the fix. The 315-mark shortfall is 35% of the 900 maximum but 70% of the 450 R actually scored.

Every percentage question turns on the phrase 'per cent of what'. Three different bases live in this one item, and each gives a different number.

The maximum (900) is the base for the target and for the miss. The score (450) is the base for the increment, because you are raising his marks from where they are.

So the same 315 marks is 35% of the maximum and 70% of the score. Decide the base before you divide.

Key facts

• R scored 450 out of a 900 maximum, which is 50% — exactly 35 percentage points below his 85% target.
• The target in marks is 765, because 85% of 900 is 765.
• A percentage increment is always taken on the starting value, so 315 more marks on a base of 450 is a 70% increase.

Common traps

• Dividing the 315-mark shortfall by the target (765) or the maximum (900) instead of the score
• Reading 'misses by 35%' as 35% of the target and then rounding 53.8 to 53
• Assuming the maximum is 100 or 500 because the stem does not name it

No directly related past PYQ was found.