A certain number of persons can complete a piece of work in 46 days. If there were 8 persons more, the work could be finished in 16 days less. How many persons were originally there ?

Options

A. 25
B. 18
C. 15
D. 20

Answer

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

### Step 1: Define the Variables
Let the original number of persons be \( x \).

### Step 2: Establish the Work Equation
The total work can be expressed in terms of the number of persons and the number of days they take to complete the work. If \( x \) persons can complete the work in 46 days, the total work \( W \) can be given by:
\[ W = x \times 46 \]

### Step 3: Set Up the New Work Equation
If there are 8 more persons, the total number of persons becomes \( x + 8 \). According to the problem, with these additional persons, the work can be finished in 30 days (16 days less than 46 days). Thus, the work can also be expressed as:
\[ W = (x + 8) \times 30 \]

### Step 4: Set the Two Expressions for Work Equal
Since both expressions represent the same total work \( W \), we can set them equal to each other:
\[ x \times 46 = (x + 8) \times 30 \]

### Step 5: Expand and Simplify the Equation
Expanding the right side:
\[ 46x = 30x + 240 \]
Now, subtract \( 30x \) from both sides:
\[ 46x - 30x = 240 \]
This simplifies to:
\[ 16x = 240 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 16:
\[ x = \frac{240}{16} = 15 \]

### Conclusion
The original number of persons is \( 15 \).

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