A and B undertook a work for Rs. 2200. A alone can do the work in 10 days and B alone can do the same work in 12 days. If they work together, what will be the difference( in Rs.) in the amount they receive?

Options

A. 350
B. 250
C. 200
D. 300

Answer

To solve the problem step by step, we will first determine the work done by A and B individually, then find their efficiencies, and finally calculate their earnings based on their efficiencies.

### Step 1: Determine the work done by A and B
- A can complete the work in 10 days.
- B can complete the work in 12 days.

### Step 2: Calculate the efficiency of A and B
- Efficiency is calculated as the amount of work done in one day.
- Work done by A in one day = 1/10 of the work.
- Work done by B in one day = 1/12 of the work.

### Step 3: Find the combined efficiency
- To find the combined efficiency, we need to find a common denominator:
- A's efficiency = 1/10 = 6/60
- B's efficiency = 1/12 = 5/60
- Combined efficiency of A and B = (6/60 + 5/60) = 11/60 of the work per day.

### Step 4: Calculate the ratio of their efficiencies
- The ratio of their efficiencies = A's efficiency : B's efficiency = 6 : 5.

### Step 5: Calculate the total earnings
- Total earnings for the work = Rs. 2200.
- The earnings are distributed in the ratio of their efficiencies (6:5).
- Total parts = 6 + 5 = 11 parts.

### Step 6: Calculate the value of one part
- Value of one part = Total earnings / Total parts = 2200 / 11 = Rs. 200.

### Step 7: Calculate the earnings of A and B
- Earnings of A = 6 parts = 6 * 200 = Rs. 1200.
- Earnings of B = 5 parts = 5 * 200 = Rs. 1000.

### Step 8: Calculate the difference in their earnings
- Difference = Earnings of A - Earnings of B = 1200 - 1000 = Rs. 200.

### Final Answer
The difference in the amount they receive is Rs. 200.

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