A certain number of persons can finish a task in 85 days. If there were 15 persons more. it would have taken 25 days less for the task to be completed. How many persons are there in the beginning?

Options

A. a) 30
B. b) 45
C. c) 40
D. d) 36

Answer

To solve the problem step by step, let's denote the number of persons in the beginning as \( M \).

### Step 1: Establish the relationship between work, persons, and days.
The total work done can be expressed in terms of persons and days. If \( M \) persons can complete the work in 85 days, then the total work can be represented as:
\[ \text{Total Work} = M \times 85 \]

### Step 2: Set up the equation for the scenario with 15 more persons.
If there are 15 more persons, the total number of persons becomes \( M + 15 \), and the time taken to complete the work decreases by 25 days, making it 60 days. Thus, the work can also be expressed as:
\[ \text{Total Work} = (M + 15) \times 60 \]

### Step 3: Equate the two expressions for total work.
Since both expressions represent the same total work, we can set them equal to each other:
\[ M \times 85 = (M + 15) \times 60 \]

### Step 4: Expand and simplify the equation.
Expanding the right-hand side gives:
\[ 85M = 60M + 900 \]

### Step 5: Rearrange the equation to isolate \( M \).
Subtract \( 60M \) from both sides:
\[ 85M - 60M = 900 \]
This simplifies to:
\[ 25M = 900 \]

### Step 6: Solve for \( M \).
Now, divide both sides by 25:
\[ M = \frac{900}{25} = 36 \]

### Conclusion:
The number of persons in the beginning is \( M = 36 \).