Raghu agrees to complete a work for 8.400 in 16 days. But by engaging an assistant, the work is complete in 12 days. Find the share of money remuneration to be received by the assitant.

Options

A. Rs2,100
B. Rs2,500
C. Rs 2, 000
D. Rs 2, 400

Answer

To solve the problem step by step, we will first determine the total work done, then calculate the efficiencies of Raghu and the assistant, and finally find the share of remuneration for the assistant.

### Step 1: Determine the total work
Raghu can complete the work in 16 days. If we assume the total work is represented in terms of "work units," we can find the total work by taking the least common multiple (LCM) of the days taken by Raghu and the days taken when assisted.

- Raghu's work rate = Total work / Days taken by Raghu = Total work / 16 days

When Raghu works with the assistant, they complete the work in 12 days.

- Combined work rate = Total work / Days taken together = Total work / 12 days

To find the total work, we can set the total work equal to the LCM of the days taken by Raghu (16) and the days taken together (12).

**Total Work = LCM(16, 12) = 48 work units**

### Step 2: Calculate Raghu's work rate
Now, we can calculate how much work Raghu can do in one day.

- Raghu's work in one day = Total work / Days taken by Raghu = 48 / 16 = 3 work units per day

### Step 3: Calculate combined work rate
Next, we calculate how much work Raghu and the assistant can do together in one day.

- Combined work in one day = Total work / Days taken together = 48 / 12 = 4 work units per day

### Step 4: Calculate the assistant's work rate
Now, we can find the work rate of the assistant by subtracting Raghu's work rate from the combined work rate.

- Assistant's work in one day = Combined work in one day - Raghu's work in one day = 4 - 3 = 1 work unit per day

### Step 5: Determine the share of remuneration
The total remuneration for the work is ₹8,400. We need to find out what fraction of the total work was done by the assistant.

- Total work done by the assistant = 1 work unit
- Total work done by both = 4 work units (combined rate)

The share of the assistant in the remuneration can be calculated as follows:

- Assistant's share of remuneration = (Assistant's work / Total work done) * Total remuneration
- Assistant's share = (1 / 4) * 8400 = ₹2,100

### Final Answer
The share of money remuneration to be received by the assistant is **₹2,100**.

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