Twenty two men can complete a piece of work in 17 days. They work for 2 days. How many more men should now be employed so as to complete the work in another 10 days?

Options

A. 11
B. 22
C. 33
D. none of these

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Calculate the total work in man-days
Given that 22 men can complete the work in 17 days, we can calculate the total work in man-days.

\[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} = 22 \text{ men} \times 17 \text{ days} = 374 \text{ man-days} \]

### Step 2: Calculate the work done in 2 days
Next, we need to find out how much work is done by 22 men in 2 days.

\[ \text{Work Done in 2 Days} = 22 \text{ men} \times 2 \text{ days} = 44 \text{ man-days} \]

### Step 3: Calculate the remaining work
Now, we can find out how much work is left after the first 2 days.

\[ \text{Remaining Work} = \text{Total Work} - \text{Work Done in 2 Days} = 374 \text{ man-days} - 44 \text{ man-days} = 330 \text{ man-days} \]

### Step 4: Calculate the work that needs to be done in 10 days
We need to complete the remaining work in 10 days. Let \( x \) be the number of additional men needed. The total number of men working will be \( 22 + x \).

The equation for the work done in 10 days by \( 22 + x \) men is:

\[ (22 + x) \text{ men} \times 10 \text{ days} = 330 \text{ man-days} \]

### Step 5: Set up the equation
From the above, we can set up the equation:

\[ 10(22 + x) = 330 \]

### Step 6: Solve for \( x \)
Now, we can simplify and solve for \( x \):

\[ 220 + 10x = 330 \]

Subtract 220 from both sides:

\[ 10x = 330 - 220 \]
\[ 10x = 110 \]

Now, divide by 10:

\[ x = 11 \]

### Conclusion
Thus, the number of additional men that should be employed is \( \boxed{11} \).

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