A and B's work units given.They were together gievn Rs.720.When C joined,they together completed the work in 5 days.Find C's wages

To solve the problem of determining C's wages, we first need to understand the work dynamics between A, B, and C. Let's break down the information step by step.

Understanding the Work Contribution

We know that A and B were initially given Rs. 720 for their work. When C joined them, they completed the work together in 5 days. To find C's wages, we need to determine how much work A, B, and C contributed to the project.

Step 1: Determine A and B's Work Rate

Let’s assume A can complete the work in 'a' days and B can complete it in 'b' days. Therefore, their work rates can be expressed as:

• A's work rate = 1/a (work units per day)
• B's work rate = 1/b (work units per day)

When A and B work together, their combined work rate is:

Combined work rate of A and B = 1/a + 1/b

Step 2: Calculate Total Work Done

Let’s denote the total work as W. Since A and B together worked for 5 days before C joined, the amount of work they completed in that time is:

Work done by A and B in 5 days = 5 * (1/a + 1/b)

Step 3: Adding C's Contribution

When C joins A and B, they complete the remaining work together in 5 days. Let’s denote C's work rate as 1/c. The total work done by A, B, and C together in those 5 days is:

Work done by A, B, and C in 5 days = 5 * (1/a + 1/b + 1/c)

Step 4: Equating Work Done

Since the total work W is the same in both scenarios, we can set the equations equal to each other:

5 * (1/a + 1/b) + 5 * (1/c) = W

Step 5: Finding C's Wages

Now, we need to find out how much of the total Rs. 720 should be allocated to C. To do this, we can calculate the ratio of C's work contribution to the total work done by A, B, and C.

Let’s assume the total work done by A and B is W1 and the work done by C is W2. The ratio of C's work to the total work can be expressed as:

Ratio of C's work = W2 / (W1 + W2)

Then, C's wages can be calculated as:

C's wages = Total wages * (C's work ratio)

Example Calculation

For a concrete example, let’s assume A and B together can complete the work in 10 days (A = 10, B = 10). Thus:

• Combined work rate of A and B = 1/10 + 1/10 = 1/5
• Work done by A and B in 5 days = 5 * (1/5) = 1 unit of work

If C can complete the work in 5 days, then:

• C's work rate = 1/5
• Work done by C in 5 days = 5 * (1/5) = 1 unit of work

Now, the total work done is 2 units. The ratio of C's work is 1/2, so:

C's wages = 720 * (1/2) = Rs. 360

In summary, to find C's wages, we need to analyze the work contributions of A, B, and C, calculate their respective work rates, and then determine the appropriate share of the total payment based on their contributions. This method ensures that each worker is compensated fairly for their efforts.