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?

• Let the total adult population be 100, with 50 men and 50 women (assuming equal gender distribution as is standard in such problems unless specified otherwise, or simply let total be $N$ and men be $M$, women be $W$; however, the problem implies a specific ratio or standard assumption. Let's assume 50 men and 50 women for simplicity, or derive generally. Actually, the problem states '40% men and 30% women are married'. It does not explicitly state the gender ratio. However, in UPSC CSAT, if the gender ratio isn't given, it is often assumed to be 1:1 or the answer is independent of it? No, the percentage of the *total* population depends on the ratio. Let's re-read carefully. 'In adult population... 40% men... 30% women'. If the ratio of men to women is not 1:1, the answer changes. Let's check the options. If Men=50, Women=50: Married Men = 0.4*50 = 20. Married Women = 0.3*50 = 15. Since no polygamy, the number of married couples is limited by the smaller group, which is 15. So 15 men and 15 women are married. Total married = 30. Percentage = 30/100 = 30%. This is not an option.

• Let's reconsider the standard interpretation. Perhaps the '40% men' refers to 40% of the *total* population being married men? No, '40% men... are married' usually means 40% of the male population.

• Let's look at the options: 33 1/7% is 23/70? No, 33.33% is 1/3. 34 2/7% is 240/700 = 24/70 = 12/35 ≈ 34.28%.

• Let's assume the number of married men equals the number of married women because of the 1:1 marriage constraint. Let $M$ be total men, $W$ be total women. Married Men = $0.4M$. Married Women = $0.3W$. Since each marriage involves one man and one woman, $0.4M = 0.3W$. Therefore, $4M = 3W$, or $M/W = 3/4$.

• So, for every 3 men, there are 4 women. Let Total Men = 30, Total Women = 40. Total Population = 70.

• Number of married men = $40\%$ of $30 = 12$.

• Number of married women = $30\%$ of $40 = 12$.

• This is consistent (12 couples).

• Total married population = $12 + 12 = 24$.

• Percentage of married adult population = $(24 / 70) \times 100$.

• $24/70 = 12/35$.

• $12/35 = 0.342857...$

• Converting to mixed fraction: $12/35 = 34 \frac{2}{7} \%$ (since $12/35 = 84/245$? No. $12/35 = 0.3428$. $34 \frac{2}{7} = 34 + 0.2857 = 34.2857$. Let's check: $34 \frac{2}{7} = \frac{34 \times 7 + 2}{7} = \frac{238+2}{7} = \frac{240}{7}$. Wait. $24/70 = 12/35$. $12/35 = 24/70$. $24/70 \times 100 = 2400/70 = 240/7 = 34 \frac{2}{7}$. Yes.)

• Thus, the percentage is $34 \frac{2}{7} \%$.