Given: Himanshu completed the work = 20 days Ekram completed the work = 30 days Formula Used: Work = Time × Efficiency Calculation: Himanshu completed the work = 20 days Ekram completed the work = 30 days Let total work be LCM of (20 and 30) = 60 units ⇒ Efficiency of Himanshu = 60/20 = 3 units ⇒ Efficiency of Ekram = 60/30 = 2 units Work done by Ekram and Himanshu in 2 days working alternatively = 2 + 3 = 5 units According to the question, Himanshu left after working 5 days i.e. Himanshu and Ekram do the work alternatively till 10th day ⇒10 days work = 5 × 5 = 25 ⇒ Remaining work = 60 – 25 = 35 35 works will be done by Ekram on alternatives days 11th day work by Ekram = 2 work 12th day no work done 13th day work by Ekram ……..so on ⇒ Work done in 4 days = 4 units ⇒ 2 units of work is done in 2 days ⇒ 34 units of work will done in next 34 days ⇒ Total work done in (34 + 10) 44 days = 34 + 25 = 59 units Remaining work = 60 – 59 = 1 Time is taken by Ekram to complete 1 unit work = 1/2 days Total days to complete the work = 10 + 34 + 1/2 = 44.5 days ∴ The total time is 44.5 days