A, B and C can do a work in 20 days, 25 days and 30 days respectively. They finished together that work and gained Rs. 3700 as wage. Find the wages of A, B and C respectively.

Answer

To solve the problem, we need to find the wages of A, B, and C based on their efficiencies in completing the work. Here’s a step-by-step solution:

### Step 1: Determine the total work
The total work can be calculated using the least common multiple (LCM) of the days taken by A, B, and C to complete the work individually.

- A can complete the work in 20 days.
- B can complete the work in 25 days.
- C can complete the work in 30 days.

**LCM of 20, 25, and 30:**
- The prime factorization is:
- 20 = 2^2 * 5^1
- 25 = 5^2
- 30 = 2^1 * 3^1 * 5^1
- Taking the highest power of each prime:
- 2^2 (from 20)
- 3^1 (from 30)
- 5^2 (from 25)

Thus, LCM = 2^2 * 3^1 * 5^2 = 4 * 3 * 25 = 300.

**Total work = 300 units.**

### Step 2: Calculate the efficiency of each worker
Efficiency is calculated as the total work divided by the number of days taken by each worker.

- Efficiency of A = Total Work / Days taken by A = 300 / 20 = 15 units/day.
- Efficiency of B = Total Work / Days taken by B = 300 / 25 = 12 units/day.
- Efficiency of C = Total Work / Days taken by C = 300 / 30 = 10 units/day.

### Step 3: Calculate the total efficiency
Total efficiency of A, B, and C together is the sum of their individual efficiencies.

Total Efficiency = Efficiency of A + Efficiency of B + Efficiency of C = 15 + 12 + 10 = 37 units/day.

### Step 4: Determine the value of each unit of work
The total wages earned by A, B, and C together is Rs. 3700.

To find the value of one unit of work:
- Value of one unit = Total Wages / Total Efficiency = 3700 / 37 = Rs. 100.

### Step 5: Calculate the wages of A, B, and C
Now, we can calculate the wages for each worker based on their efficiency.

- Wages of A = Efficiency of A * Value of one unit = 15 * 100 = Rs. 1500.
- Wages of B = Efficiency of B * Value of one unit = 12 * 100 = Rs. 1200.
- Wages of C = Efficiency of C * Value of one unit = 10 * 100 = Rs. 1000.

### Final Wages
- Wages of A = Rs. 1500
- Wages of B = Rs. 1200
- Wages of C = Rs. 1000