A, B and C, each of them working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn Rs. 2340, what will be C's share of the earnings?

Options

A. Rs. 520
B. Rs.1080
C. Rs. 1170
D. Rs.630

Answer

To find C's share of the earnings when A, B, and C work together, we can follow these steps:

### Step 1: Determine the work done by A, B, and C
- A can complete the job in 6 days.
- B can complete the job in 8 days.
- C can complete the job in 12 days.

### Step 2: Calculate the total work in terms of work units
To find the total work, we can use the least common multiple (LCM) of the days taken by A, B, and C to finish the job.

The LCM of 6, 8, and 12 is 24. Therefore, we can consider the total work to be 24 units.

### Step 3: Calculate the work done by each person in one day
- Work done by A in one day = Total work / Days taken by A = 24 / 6 = 4 units
- Work done by B in one day = Total work / Days taken by B = 24 / 8 = 3 units
- Work done by C in one day = Total work / Days taken by C = 24 / 12 = 2 units

### Step 4: Calculate the total work done by A, B, and C together in one day
Total work done by A, B, and C together in one day = Work done by A + Work done by B + Work done by C
= 4 + 3 + 2 = 9 units

### Step 5: Determine C's share of the total work
C's share of the work = Work done by C / Total work done by A, B, and C together
= 2 / 9

### Step 6: Calculate C's share of the earnings
Total earnings = Rs. 2340
C's share of the earnings = C's share of work * Total earnings
= (2/9) * 2340

### Step 7: Simplify the calculation
= 2 * (2340 / 9)
= 2 * 260
= Rs. 520

Thus, C's share of the earnings is Rs. 520.

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