If six men working 8 hours a day earn Rs. 840 per week then 9 men working 6 hours a day will earn per week-----

Options

A. Rs.840
B. Rs.945
C. Rs.1620
D. Rs.1680

Answer

To solve the problem, we will first determine the total work done by the six men in a week and then find out how much work the nine men can do in a week. Finally, we will calculate their earnings based on the work done.

### Step 1: Calculate the total work done by 6 men in a week.

Given:
- Number of men = 6
- Hours worked per day = 8
- Days worked in a week = 7 (assuming a week has 7 days)

Total work done by 6 men in a week can be calculated as:
\[ \text{Total Work} = \text{Number of Men} \times \text{Hours per Day} \times \text{Days per Week} \]
\[ \text{Total Work} = 6 \times 8 \times 7 = 336 \text{ man-hours} \]

### Step 2: Calculate the earning per man-hour.

From the problem, we know that 6 men earn Rs. 840 for 336 man-hours of work.
Thus, the earning per man-hour is:
\[ \text{Earning per man-hour} = \frac{\text{Total Earnings}}{\text{Total Work}} \]
\[ \text{Earning per man-hour} = \frac{840}{336} = 2.5 \text{ Rs/man-hour} \]

### Step 3: Calculate the total work done by 9 men in a week.

Now, we need to calculate the work done by 9 men working 6 hours a day for 7 days.
\[ \text{Total Work by 9 men} = 9 \times 6 \times 7 = 378 \text{ man-hours} \]

### Step 4: Calculate the earnings for 9 men.

Now, we can find out how much 9 men will earn for 378 man-hours of work.
\[ \text{Total Earnings} = \text{Total Work} \times \text{Earning per man-hour} \]
\[ \text{Total Earnings} = 378 \times 2.5 = 945 \text{ Rs} \]

### Final Answer:
Thus, 9 men working 6 hours a day will earn Rs. 945 per week.

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