Question

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?

• A. 9 days
• B. 18 days
• C. 12 days
• D. 8 days

Answer 1

Answer:

D. 8 days

A's work rate = 1/11 (sari per day) B's work rate = 1/20 (sari per day) C's work rate = 1/55 (sari per day) Combined work rate of A and B = (1/11) + (1/20) = (20 + 11) / 220 = 31/220 (sari per day) Combined work rate of A and C = (1/11) + (1/55) = (5 + 1) / 55 = 6/55 (sari per day) Work done in 2 days = (31/220) + (6/55) = (31/220) + (24/220) = 55/220 = 1/4 (sari) Since 1/4 of the work is done in 2 days, it will take approximately 4 cycles to complete the work. So, 4 cycles * 2 days/cycle = 8 days. Work done in 8 days = 4 cycles * (1/4 sari/cycle) = 1 sari. The work can be completed in 8 days.