Question

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?

• A. 5
• B. 6
• C. 7
• D. 9

Answer 1

The Correct Option is B

Let the amount of work that 1 man can do in 1 day be \( M \) and the amount of work that 1 woman can do in 1 day be \( W \).

• From the information that 6 men alone can complete the work in 3 days, the total work done by 6 men in 1 day is: \[ 6M \times 3 = 1 \quad \Rightarrow \quad 6M = \frac{1}{3} \quad \Rightarrow \quad M = \frac{1}{18} \] Thus, 1 man does \( \frac{1}{18} \) of the work in 1 day.
• For 3 men and 18 women working together for 2 days, the total work done is: \[ (3M + 18W) \times 2 = 1 \]

Substitute \( M = \frac{1}{18} \):

\[ \left(3 \times \frac{1}{18} + 18W\right) \times 2 = 1 \quad \Rightarrow \quad \left(\frac{3}{18} + 18W\right) \times 2 = 1 \]

\[ \left(\frac{1}{6} + 18W\right) \times 2 = 1 \quad \Rightarrow \quad \frac{1}{3} + 36W = 1 \quad \Rightarrow \quad 36W = \frac{2}{3} \quad \Rightarrow \quad W = \frac{1}{54} \]

• Now, for 9 women working alone: \[ 9W \times D = 1 \quad \Rightarrow \quad 9 \times \frac{1}{54} \times D = 1 \quad \Rightarrow \quad D = 6 \]

Thus, 9 women will take 6 days to complete the work.