arithmetic - phani and shasi together can do a piece of work in 12 days which shasi and vani together can do in 16 days after phani has been working at it for 5 days and shasi for 7 days vani finishes it in 24 days in how many days vani will alone will do - skillgun

Solution: Let P = Phani, Q = Shasi, R = Vani.
P's 5 days work + Q's 7 days work + R's 24 days work =1.
=> (P+Q)'s 5 days work + (Q+R)'s 2 days work + R's 22 days work = 1
=> 5/12 + 2/16 + R's 22 Days work = 1.
=> R's 1 day's work = 1-(5/12 + 2/16) = 11/24
=> R's 1 day's work = (11/24 * 1/22) = 1/48.
.'. R alone can finish the work in 48 days.