If 10 men can complete a piece of work in 12 days by working 7 hours a day, then in how many days can 14 mendo the same work by working 6 hours a day?

Options

A. A. 16
B. B. 15
C. C. 10
D. D. 12

Answer

To solve the problem step by step, we can use the concept of work done, which is represented by the formula:

\[ \text{Work} = \text{Men} \times \text{Days} \times \text{Hours} \]

### Step 1: Calculate the total work done by 10 men in 12 days working 7 hours a day.

Using the formula:

\[ \text{Total Work} = \text{Men} \times \text{Days} \times \text{Hours} \]

Substituting the values:

\[ \text{Total Work} = 10 \, \text{men} \times 12 \, \text{days} \times 7 \, \text{hours} = 840 \, \text{man-hours} \]

### Step 2: Set up the equation for the new scenario with 14 men working 6 hours a day.

Let \( D \) be the number of days required for 14 men to complete the same work while working 6 hours a day. The equation will be:

\[ \text{Total Work} = 14 \, \text{men} \times D \, \text{days} \times 6 \, \text{hours} \]

### Step 3: Equate the total work from both scenarios.

Since the total work remains the same, we can set the two expressions for total work equal to each other:

\[ 840 \, \text{man-hours} = 14 \, \text{men} \times D \, \text{days} \times 6 \, \text{hours} \]

### Step 4: Simplify the equation to find \( D \).

First, calculate \( 14 \times 6 \):

\[ 14 \times 6 = 84 \]

Now we can rewrite the equation:

\[ 840 = 84D \]

To find \( D \), divide both sides by 84:

\[ D = \frac{840}{84} = 10 \]

### Conclusion:

The number of days required for 14 men to complete the work by working 6 hours a day is **10 days**.

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