Final answer:
B's share of the Rs. 6600 payment for the work completed with A is Rs. 2200. This is calculated based on the proportion of work completed by B compared to A, considering their individual work rates and the amount of time each spent working on the project.
Step-by-step explanation:
To solve how much B's share is from the total payment of Rs. 6600 for the work done together with A, we need to calculate the amount of work each person did. First, we determine each person's work rate: A can finish the work in 12 days, which means A does 1/12 of the work per day. Similarly, B finishes in 15 days, which means B's rate is 1/15 of the work per day.
When they work together, they combine their rates, doing 1/12 + 1/15 = 5/60 + 4/60 = 9/60 = 3/20 of the work per day. Now, since A finished the remaining work in 3 days alone, A did 3 * (1/12) = 1/4 of the work in those last 3 days. Subtracting A's solo work from the total, we have 3/4 of the work that was completed together.
We now determine how many days they worked together. Since they did 3/4 of the work together at the rate of 3/20 per day, we calculate (3/4) / (3/20) = (3/4) * (20/3) = 5 days together. Then, A's total days of work is 5 + 3 = 8 days, and B's is 5 days. Total work units done by A and B are 8 * (1/12) for A and 5 * (1/15) for B.
To find out how much each should get paid, we compare their work units. A's work units are 8/12 = 2/3, and B's are 5/15 = 1/3. Since the payment is Rs. 6600, B should receive (1/3) of Rs. 6600, which equals Rs. 2200.