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

To solve this problem, we need to determine the number of days 9 women alone would take to complete a piece of work, given specific conditions about men and women working together. 

1. Let's first calculate the total work done in terms of "man-days" or "woman-days". According to the question, \(3\) men and \(18\) women can complete the work in \(2\) days.
2. Assume the work done by one man in one day is \(M\), and by one woman is \(W\).
3. The total work in terms of man-woman-days is: \(2 \times (3M + 18W)\)
4. Given that \(6\) men alone take \(3\) days to complete the work, we have: \(Work = 3 \times 6M = 18M\)
5. Equating this to the work done by men and women together: \(2 \times (3M + 18W) = 18M\)
6. Simplifying the equation: \(6M + 36W = 18M\)
7. Rearranging gives: \(12M = 36W\) or \(M = 3W\)
8. We can now express \(M\) in terms of \(W\). As \(M = 3W\), substitute into the equation for work to get: \(18M = 18 \times 3W = 54W\)
9. This indicates the work can also be expressed as \(54\) "woman-days".
10. For \(9\) women to complete the same work: \(\text{Number of Days} = \frac{54W}{9W} = 6\) days

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

Thus, the correct answer is

6

.

 

Answer 2

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.