Q11
3 men and 18 women together take 2 days to complete a piece of work. How many days will 9 women alone take to complete the piece of work; if 6 men alone can complete the piece of work in 3 days?
Answer: B
Asked: the days 9 women alone need.
6 men finish in 3 days, so the work = 18 man-days. One man does 1/18 of the work per day.
3 men + 18 women finish in 2 days: \( 2\left(\frac{3}{18} + 18w\right) = 1 \).
\( \frac{1}{6} + 18w = \frac{1}{2} \), so \( 18w = \frac{1}{3} \) and \( w = \frac{1}{54} \).
9 women do 9/54 = 1/6 of the work per day, so they need 6 days.
Alternative: 1 man = 3 women (1/18 vs 1/54). Then 3 men + 18 women = 27 women, who take 2 days. So 9 women take 2 × 27/9 = 6 days.
Answer: 6