A alone can do a piece of work in 12 days and B can do the same work in 15 days. If they complete the work together and receive a total amount of Rs. 1800, then find the share of B.

Options

A. RS.700
B. 800
C. 900
D. 1000

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the work done by A and B

A can complete the work in 12 days, and B can complete the same work in 15 days.

### Step 2: Find the total work in terms of units

To find a common measure of work, we can calculate the Least Common Multiple (LCM) of 12 and 15.

- LCM of 12 and 15 = 60 units

This means we can consider the total work to be 60 units.

### Step 3: Calculate the work done by A and B per day

- Work done by A in one day = Total work / Days taken by A = 60 units / 12 days = 5 units/day
- Work done by B in one day = Total work / Days taken by B = 60 units / 15 days = 4 units/day

### Step 4: Calculate the total work done together in one day

When A and B work together in one day, they complete:
- Total work done together = Work done by A + Work done by B = 5 units + 4 units = 9 units/day

### Step 5: Calculate the total amount received and the share of each worker

The total amount received for the work is Rs. 1800. We need to find out how much share B will get.

Let’s denote the share of A as 5x and the share of B as 4x, where x is the amount earned per unit of work done.

### Step 6: Set up the equation

The total amount received can be expressed as:
- 5x + 4x = 1800
- 9x = 1800

### Step 7: Solve for x

To find the value of x, divide both sides by 9:
- x = 1800 / 9
- x = 200

### Step 8: Calculate B's share

Now we can find B's share:
- B's share = 4x = 4 * 200 = Rs. 800

### Conclusion

Thus, B's share of the total amount is Rs. 800.

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