If 20 persons can do a piece of work in 7 days, then the number of persons required to complete the work in 28 days:

Options

A. 4
B. 5
C. 14
D. 10

Answer

To solve the problem step by step, we can use the concept of inverse proportion. Here’s how we can approach the question:

### Step 1: Understand the relationship
We know that if 20 persons can complete a piece of work in 7 days, then the number of persons required will change if the number of days changes. Since the number of persons and the number of days are inversely proportional, we can set up a relationship.

### Step 2: Set up the equation
Let \( P_1 \) be the number of persons (20) and \( D_1 \) be the number of days (7). We need to find \( P_2 \) (the number of persons required) when \( D_2 \) is 28 days.

Using the inverse proportion formula:
\[ P_1 \times D_1 = P_2 \times D_2 \]

### Step 3: Substitute the known values
Substituting the known values into the equation:
\[ 20 \times 7 = P_2 \times 28 \]

### Step 4: Calculate the left side
Calculate \( 20 \times 7 \):
\[ 20 \times 7 = 140 \]
So now we have:
\[ 140 = P_2 \times 28 \]

### Step 5: Solve for \( P_2 \)
To find \( P_2 \), divide both sides of the equation by 28:
\[ P_2 = \frac{140}{28} \]

### Step 6: Simplify the fraction
Now simplify \( \frac{140}{28} \):
\[ P_2 = 5 \]

### Conclusion
Thus, the number of persons required to complete the work in 28 days is **5 persons**.

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