A,B,C can do a work in 20,25,30 days respectively they undertook to finish the work together o Rs.2220 then the shame of A exceeds that of B by

Options

A. Rs.120
B. Rs.180
C. Rs.300
D. Rs.600

Answer

To solve the problem step by step, we need to determine how much more A earns compared to B when they work together.

### Step 1: Determine the Work Done by A, B, and C
A can complete the work in 20 days, B in 25 days, and C in 30 days. To find the total work, we will calculate the Least Common Multiple (LCM) of the days they take.

**Calculation of LCM:**
- The LCM of 20, 25, and 30 is 300.

### Step 2: Calculate the Efficiency of Each Worker
Efficiency is defined as the amount of work done in one day. We can calculate the efficiency of A, B, and C using the formula:

\[ \text{Efficiency} = \frac{\text{Total Work}}{\text{Number of Days}} \]

- Efficiency of A:
\[ \text{Efficiency of A} = \frac{300}{20} = 15 \]
- Efficiency of B:
\[ \text{Efficiency of B} = \frac{300}{25} = 12 \]
- Efficiency of C:
\[ \text{Efficiency of C} = \frac{300}{30} = 10 \]

### Step 3: Calculate Total Efficiency
Now, we can find the total efficiency when A, B, and C work together:

\[ \text{Total Efficiency} = \text{Efficiency of A} + \text{Efficiency of B} + \text{Efficiency of C} = 15 + 12 + 10 = 37 \]

### Step 4: Determine the Earnings Based on Efficiency
The total payment for completing the work is Rs. 2220. The share of each worker is proportional to their efficiency.

To find the value of one unit of efficiency:

\[ \text{Value of 1 Efficiency} = \frac{2220}{37} \approx 60 \]

### Step 5: Calculate the Earnings of A and B
Now, we can calculate the earnings of A and B:

- Earnings of A:
\[ \text{Earnings of A} = \text{Efficiency of A} \times \text{Value of 1 Efficiency} = 15 \times 60 = 900 \]
- Earnings of B:
\[ \text{Earnings of B} = \text{Efficiency of B} \times \text{Value of 1 Efficiency} = 12 \times 60 = 720 \]

### Step 6: Find the Difference in Earnings
Finally, we find how much more A earns compared to B:

\[ \text{Difference} = \text{Earnings of A} - \text{Earnings of B} = 900 - 720 = 180 \]

### Conclusion
The share of A exceeds that of B by Rs. 180.

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