A man completes a work in 10 days by doing 5 hours per day. By doing 7 hours per day, he can complete this work in -

Options

A. 12 days
B. 10 days
C. 7 days
D. None of these

Answer

To solve the problem step by step, we will use the formula that relates the amount of work done in terms of man-days and hours worked.

### Step 1: Understand the given information
- A man completes a work in 10 days by doing 5 hours per day.
- We need to find out how many days he will take to complete the same work if he works 7 hours per day.

### Step 2: Define the variables
- Let \( M_1 \) = 1 (the man)
- \( D_1 \) = 10 days (the time taken in the first scenario)
- \( H_1 \) = 5 hours (the hours worked per day in the first scenario)

In the second scenario:
- \( M_2 \) = 1 (the same man)
- \( D_2 \) = ? (the time taken in the second scenario, which we need to find)
- \( H_2 \) = 7 hours (the hours worked per day in the second scenario)

### Step 3: Use the formula
The formula relating the work done is:
\[ M_1 \times D_1 \times H_1 = M_2 \times D_2 \times H_2 \]

### Step 4: Substitute the known values
Substituting the known values into the formula:
\[ 1 \times 10 \times 5 = 1 \times D_2 \times 7 \]
This simplifies to:
\[ 50 = D_2 \times 7 \]

### Step 5: Solve for \( D_2 \)
To find \( D_2 \), divide both sides by 7:
\[ D_2 = \frac{50}{7} \]

### Step 6: Calculate \( D_2 \)
Calculating \( D_2 \):
\[ D_2 \approx 7.14 \text{ days} \]

Thus, the man can complete the work in approximately \( \frac{50}{7} \) days or about 7.14 days.

### Final Answer
The man can complete the work in \( \frac{50}{7} \) days.

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