'P', 'Q', and 'R' can individually complete a task in 20, 24, and 30 days, respectively. They all started working together, but 'P' stopped after 4 days. Additionally, 'R' stopped working 3 days prior to the task's completion. How many days did it take to finish the task?

Let the total task = 120 units (LCM of 20, 24 and 30) Amount of task done by P alone in one day = 120/20 = 6 units Amount of task done by Q alone in one day = 120/24 = 5 units Amount of task done by R alone in one day = 120/30 = 4 units Amount of task done by all of them together in 4 days = 4 × (6 + 5 + 4) = 60 units Amount of task done by Q alone in 3 days = 3 × 5 = 15 units Amount of task done by Q and R together in middle = 120 – 60 – 15 = 45 units Time taken by Q and R together to complete 45 units task = 45/ (5 + 4) = 45/9 = 5 units So total time taken to complete the task = 5 + 4 + 3 = 12 days