A and B do `((3)/(5))` th part of a work and the rest of the work is completed by C. If A, B and C take the same work for Rs. 5000, then what is the share fo C (in Rs.)?

Options

A. 3000
B. 2500
C. 2000
D. 1500

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the total work and the contributions of A, B, and C
A and B together complete \( \frac{3}{5} \) of the work, and C completes the remaining work.

### Step 2: Calculate the work done by C
Since A and B complete \( \frac{3}{5} \) of the work, the fraction of work completed by C is:
\[ 1 - \frac{3}{5} = \frac{2}{5} \]
This means C completes \( \frac{2}{5} \) of the total work.

### Step 3: Determine the total payment for the work
The total payment for the work done by A, B, and C is Rs. 5000.

### Step 4: Calculate the share of A and B
Since A and B together completed \( \frac{3}{5} \) of the work, their share of the payment can be calculated as follows:
\[ \text{Share of A and B} = \text{Total Payment} \times \frac{3}{5} = 5000 \times \frac{3}{5} \]
Calculating this gives:
\[ 5000 \times \frac{3}{5} = 5000 \times 0.6 = 3000 \]
So, A and B together receive Rs. 3000.

### Step 5: Calculate the share of C
To find C's share, we subtract the amount received by A and B from the total payment:
\[ \text{Share of C} = \text{Total Payment} - \text{Share of A and B} = 5000 - 3000 \]
Calculating this gives:
\[ 5000 - 3000 = 2000 \]
Thus, C's share is Rs. 2000.

### Final Answer
The share of C is Rs. 2000.

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