6 women can complete a work in 46 hours. In how many hours will 23 women complete that work?

Options

A. 18
B. 16
C. 12
D. 24

Answer

To solve the problem of how many hours 23 women will take to complete the same work that 6 women can complete in 46 hours, we can follow these steps:

### Step 1: Determine the total work done in terms of "woman-hours."
The total work can be calculated by multiplying the number of women by the time taken.
- For 6 women working for 46 hours:
\[ \text{Total Work} = \text{Number of Women} \times \text{Time} = 6 \text{ women} \times 46 \text{ hours} = 276 \text{ woman-hours} \]

### Step 2: Calculate the efficiency of 23 women.
Now, we need to find out how long it will take for 23 women to complete the same amount of work (276 woman-hours).
- Let \( T \) be the time taken by 23 women to complete the work.
- The total work done by 23 women in \( T \) hours is:
\[ \text{Work} = 23 \text{ women} \times T \text{ hours} \]

### Step 3: Set the equations equal to each other.
Since the total work done is the same, we can set the two expressions for work equal to each other:
\[ 23 \times T = 276 \]

### Step 4: Solve for \( T \).
To find \( T \), divide both sides of the equation by 23:
\[ T = \frac{276}{23} \]
Calculating this gives:
\[ T = 12 \text{ hours} \]

### Conclusion:
Thus, 23 women will complete the work in **12 hours**.

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