Sandy and Mandy do `(8/13)`th part of a work and the rest of the work was completed by Andy. If Sandy, Mandy and Andy take the same work for Rs. 2600. then what is the share (in Rs.) of Andy?

Options

A. 1600
B. 1400
C. 800
D. 1000

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the fraction of work completed by Andy
Sandy and Mandy together completed \( \frac{8}{13} \) of the work. Therefore, the fraction of work completed by Andy is:
\[ \text{Work done by Andy} = 1 - \frac{8}{13} = \frac{13}{13} - \frac{8}{13} = \frac{5}{13} \]

### Step 2: Calculate the total payment for the work
The total payment for the work done by Sandy, Mandy, and Andy is Rs. 2600.

### Step 3: Determine the share of each worker based on the work done
Since the payment is distributed based on the amount of work done, we need to find the total parts of work done by all three workers.

- Sandy and Mandy together did \( \frac{8}{13} \) of the work.
- Andy did \( \frac{5}{13} \) of the work.

The total work can be expressed in terms of parts:
- Total parts of work = \( \frac{8}{13} + \frac{5}{13} = \frac{13}{13} = 1 \)

### Step 4: Calculate the share of Andy
To find Andy's share, we need to calculate the fraction of the total payment that corresponds to the work done by Andy:
\[ \text{Andy’s share} = \text{Total payment} \times \frac{\text{Work done by Andy}}{\text{Total work}} = 2600 \times \frac{5/13}{1} \]

Calculating Andy's share:
\[ \text{Andy’s share} = 2600 \times \frac{5}{13} = 2600 \div 13 \times 5 \]
Calculating \( 2600 \div 13 \):
\[ 2600 \div 13 = 200 \]
Now, multiplying by 5:
\[ \text{Andy’s share} = 200 \times 5 = 1000 \]

### Final Answer
Thus, Andy's share in Rs. is:
\[ \text{Andy’s share} = 1000 \]

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