In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?
- (a) 33 1/7 %
- (b) 34%
- (c) 34 2/7 % ✓ UPSC's answer
- (d) 35%
Why the answer is (c)
• Each marriage pairs one man with one woman, so married men = married women.
• If there are M men and W women, 0·4M = 0·3W, so M : W = 3 : 4.
• Take 30 men and 40 women (70 adults): married men = 12 and married women = 12, i.e. 24 married adults.
• 24/70 × 100 = 240/7 = 34 2/7 %.
• Hence option (c).
Why the other options are wrong
- (a) 33 1/7 %
- 33 1/7% corresponds to a 1/3 ratio, which would require different gender proportions or marriage rates not supported by the 40:30 constraint.
- (b) 34%
- 34% is an approximation of the correct value but lacks the precise fractional component derived from the 3:4 gender ratio.
- (d) 35%
- 35% is higher than the calculated 34.28% and does not match the exact fraction 240/7.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.