A can finish painting a sari in 11 days, B in 20 days, and C in 55 days if they work independently. In how many days can the work be completed if A is assisted by B on every odd-numbered day and by C on every even- numbered day till the work completes?

Explanation

Let's solve this problem step-by-step to find the correct answer of 8 days. Step 1: Determine the work rate of each person. A can complete the work in 11 days, so A's rate of work is 1/11 of the work per day. B can complete the work in 20 days, so B's rate of work is 1/20 of the work per day. C can complete the work in 55 days, so C's rate of work is 1/55 of the work per day. Step 2: Calculate the combined work done on odd and even days. On odd-numbered days, A and B work together, so their combined rate is: A + B = 1/11 + 1/20 = (20 + 11) / 220 = 31/220 of the work per day. On even-numbered days, A and C work together, so their combined rate is: A + C = 1/11 + 1/55 = (5 + 1) / 55 = 6/55 of the work per day. Step 3: Calculate the work done in two days (one cycle of odd + even days). In two days, the combined work done is: 31/220 + 6/55 Convert 6/55 to have a common denominator with 31/220 : 6/55 = 24/220 Therefore, the total work done in two days is: (31 + 24) / 220 = 55/220 = 1/4 of the work. Step 4: Calculate how many such cycles are needed to complete the work. Since 1/4 of the work is done in two days, it will take 4 cycles to complete the work. 4 cycles * 2 days per cycle = 8 days