'N,' 'V,' and 'R' have individual work completion times of 140 days, 112 days, and 80 days, respectively. They all started working together on a task, but after 12 days, 'N' left working, and 'R' also left the job 16 days before the task's completion. Calculate how many days 'V' worked on the task.

ATQ,   Let the total work be 560 units (LCM of 140, 112 and 80)   Amount of work done by N alone in one day = 560/140 = 4 units   Amount of work done by V alone in one day = 560/112 = 5 units   Amount of work done by R alone in one day = 560/80 = 7 units   Amount of work done by N, V and R together in 12 days = 12 × (4 + 5 + 7) = 192 units   Amount of work done by V alone in 16 days = 16 × 5 = 80 units   Remaining work = 560 – 192 – 80 = 288 units   Time taken by V and R together to complete 288 units work = 288/(7 + 5) = 24 days   So, the number days for which V worked = 12 + 16 + 24 = 52 days