Understanding Work Rates

First, we determine the rate at which each person works. The rate is the fraction of the task completed per day.

• A's rate = $\frac{1}{20}$ task per day.
• B's rate = $\frac{1}{15}$ task per day.

Calculating Combined Work

Next, we find the combined work rate of A and B when they work together.

• Combined rate of A and B = Rate$_A$ + Rate$_B$ = $\frac{1}{20} + \frac{1}{15}$
• To add these fractions, find a common denominator (60): $\frac{3}{60} + \frac{4}{60} = \frac{7}{60}$ task per day.

Work Done by A and B

A and B worked together for 5 days. Calculate the total work they completed.

• Work done by A and B in 5 days = Combined rate $\times$ Days worked = $\frac{7}{60} \times 5 = \frac{35}{60} = \frac{7}{12}$ task.

Remaining Work and C's Contribution

Determine the portion of the task left after A and B stopped, and how C completed it.

• Remaining work = Total work - Work done by A and B = $1 - \frac{7}{12} = \frac{5}{12}$ task.
• C finished this remaining $\frac{5}{12}$ task in 2 days.
• C's rate = $\frac{\text{Remaining work}}{\text{Days C worked}} = \frac{5/12}{2} = \frac{5}{24}$ task per day.

Distributing the Total Payment

The total payment of ₹2,400 is distributed based on the actual amount of work done by each person.

• Work done by A in 5 days = Rate$_A \times$ Days worked $= \frac{1}{20} \times 5 = \frac{5}{20} = \frac{1}{4}$ task.
• Work done by B in 5 days = Rate$_B \times$ Days worked $= \frac{1}{15} \times 5 = \frac{5}{15} = \frac{1}{3}$ task.
• Work done by C in 2 days = $\frac{5}{12}$ task (as calculated above).
• Total Payment = ₹2,400.
• A's share of payment = (Work done by A / Total Work) $\times$ Total Payment = $\frac{1/4}{1} \times 2400 = ₹600$.
• B's share of payment = (Work done by B / Total Work) $\times$ Total Payment = $\frac{1/3}{1} \times 2400 = ₹800$.
• C's share of payment = (Work done by C / Total Work) $\times$ Total Payment = $\frac{5/12}{1} \times 2400 = ₹1000$.

Calculating Daily Wages

Now, calculate the daily wage for A and C based on their total earnings and the days they worked.

• A's daily wage = $\frac{\text{A's total payment}}{\text{Days A worked}} = \frac{₹600}{5} = ₹120$ per day.
• C's daily wage = $\frac{\text{C's total payment}}{\text{Days C worked}} = \frac{₹1000}{2} = ₹500$ per day.

Finding the Difference

Finally, calculate the difference between C's daily wage and A's daily wage.

• Difference = C's daily wage - A's daily wage = $₹500 - ₹120 = ₹380$.