To solve the problem, we need to determine the share of the amount that C earns when A, B, and C work together to complete a job. Here’s a step-by-step solution:
### Step 1: Determine the work done by A and B individually.
- A can complete the job in 15 days, so A's work rate is:
\[
\text{Work rate of A} = \frac{1}{15} \text{ (jobs per day)}
\]
- B can complete the job in 12 days, so B's work rate is:
\[
\text{Work rate of B} = \frac{1}{12} \text{ (jobs per day)}
\]
### Step 2: Calculate the combined work rate of A and B.
- The combined work rate of A and B is:
\[
\text{Combined work rate of A and B} = \frac{1}{15} + \frac{1}{12}
\]
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 15 and 12 is 60.
\[
\frac{1}{15} = \frac{4}{60}, \quad \frac{1}{12} = \frac{5}{60}
\]
- Therefore,
\[
\text{Combined work rate of A and B} = \frac{4}{60} + \frac{5}{60} = \frac{9}{60} = \frac{3}{20} \text{ (jobs per day)}
\]
### Step 3: Determine the combined work rate of A, B, and C.
- Together, A, B, and C can complete the job in 5 days, so their combined work rate is:
\[
\text{Combined work rate of A, B, and C} = \frac{1}{5} \text{ (jobs per day)} = \frac{12}{60}
\]
### Step 4: Calculate C's work rate.
- We know the combined work rate of A and B is \(\frac{3}{20}\) (or \(\frac{9}{60}\)), and the combined work rate of A, B, and C is \(\frac{12}{60}\).
- To find C's work rate, we subtract the work rate of A and B from the work rate of A, B, and C:
\[
\text{Work rate of C} = \frac{12}{60} - \frac{9}{60} = \frac{3}{60} = \frac{1}{20} \text{ (jobs per day)}
\]
### Step 5: Determine the ratio of work done by A, B, and C.
- The work rates are:
- A: \(\frac{4}{60}\)
- B: \(\frac{5}{60}\)
- C: \(\frac{3}{60}\)
- The total work done in terms of parts is:
\[
\text{Total parts} = 4 + 5 + 3 = 12 \text{ parts}
\]
### Step 6: Calculate C's share of the total amount.
- The total payment for the job is 1200 rupees. Since C's contribution is 3 parts out of 12, we can calculate C's share:
\[
\text{C's share} = \frac{3}{12} \times 1200 = \frac{1}{4} \times 1200 = 300 \text{ rupees}
\]
### Final Answer:
C's share of the amount is **300 rupees**.
