In a constituency, 45% of the total number of voters are males and the rest are females. If 60% of the males are illiterate and 60% of the females are literate, then by what per cent is the number of illiterate females more than that of literate males? (Rounded off to 2 decimal places)

Correct — D. Take the electorate as 100 voters, so every percentage becomes a headcount.

Males = 45, females = 100 − 45 = 55.
Illiterate males = 60% of 45 = 27, so literate males = 45 − 27 = 18.
Literate females = 60% of 55 = 33, so illiterate females = 55 − 33 = 22.

The phrase is "more than that of literate males", so 18 is the base, not 22 and not 100.

(22 − 18)⁄18 × 100 = 400⁄18 = 22.222… = 22.22% → option (d).

Why the others are wrong

• (a)
  30.24% — For 22 to be 30.24% more than the literate males, that count would have to be 22 ÷ 1.3024 ≈ 16.9. It is 40% of 45, which is exactly 18.
• (b)
  19.11% — The commonest slip here is comparing the other way — how much less 18 is than 22 — but that gives 4⁄22 = 18.18%, and no reading of the data produces 19.11%.
• (c)
  27.23% — 27.23% of 18 is a gap of about 4.9 voters. The real gap between illiterate females and literate males is 22 − 18 = 4.

Two traps sit inside one line of arithmetic.

First, the complement: the paper gives you the illiterate share of males and the literate share of females, so each group needs one subtraction before it is usable.

Second, the base. "A is x% more than B" always divides by B, the thing being compared to. Here B is literate males, so the denominator is 18 — never the 22, and never the 100-voter total.

Key facts

• "A is x% more than B" means x = (A − B)⁄B × 100, with B as the denominator.
• 45% male means 55% female, and 60% of males illiterate means 40% of males literate.
• Literate males = 40% of 45 = 18 and illiterate females = 40% of 55 = 22, both out of 100 voters.
• 4⁄18 = 22.22% while 4⁄22 = 18.18%, so choosing the wrong base changes the answer.

Common traps

• Dividing by 22 instead of 18 because it is the larger of the two counts
• Reading "60% of the females are literate" as the illiterate share
• Expressing the gap as a share of the 100-voter total, giving 4% instead of 22.22%

No directly related past PYQ was found.