A certain numner of men agreed to do a work in 20 days. 5 men did come for work. Others completed the work in 40 days. Find the number of men who had agreed to do the work originally.

Options

A. A) 8
B. B) 10
C. C) 12
D. D) 15

Answer

To solve the problem, we need to determine the original number of men who agreed to complete the work in 20 days. Let's break it down step by step.

### Step 1: Define Variables
Let \( x \) be the original number of men who agreed to do the work.

### Step 2: Calculate Work Done
The total work can be expressed in terms of man-days. If \( x \) men can complete the work in 20 days, the total work \( W \) is:
\[ W = x \times 20 \]

### Step 3: Determine Remaining Men
Since 5 men did not come for work, the number of men who actually worked is:
\[ x - 5 \]

### Step 4: Calculate Work Done by Remaining Men
These remaining men completed the work in 40 days. Therefore, the work done by these men can be expressed as:
\[ W = (x - 5) \times 40 \]

### Step 5: Set Up the Equation
Since the total work \( W \) is the same in both scenarios, we can set the two equations equal to each other:
\[ x \times 20 = (x - 5) \times 40 \]

### Step 6: Expand and Simplify the Equation
Expanding the right side gives:
\[ 20x = 40x - 200 \]

### Step 7: Rearrange the Equation
Rearranging the equation to isolate \( x \):
\[ 20x - 40x = -200 \]
\[ -20x = -200 \]
\[ 20x = 200 \]

### Step 8: Solve for \( x \)
Dividing both sides by 20 gives:
\[ x = 10 \]

### Conclusion
The original number of men who had agreed to do the work is \( \boxed{10} \).

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