X,Y,and Z take 20, 30 and 60 days respectively to complete a job independently. They set out to complete a job together . However Y leaves after 4 days and Z leaves after another 6 days . How many more days will it take for X alone to complete the job now?

Work rates: X=1/20, Y=1/30, Z=1/60 per day. First 4 days (all three): work done = 4*(1/20+1/30+1/60) = 4*(6/60) = 40/60. Next 6 days (X and Z): work done = 6*(1/20+1/60) = 6*(4/60) = 24/60. Total done = 64/60, but job is 60/60, so they overshot. Actually 4 days with all three + 6 days with X and Z = 10 days total. X alone needs to finish remaining work. Let me recalculate: first 4 days (X+Y+Z) = 4/10 = 2/5 work. Next 6 days (X+Z only) = 6*(1/20+1/60) = 6*(4/60) = 24/60 = 2/5. Total done = 4/5. Remaining = 1/5, which X does in (1/5)/(1/20) = 4 days.