Question

A, B and C can do a piece of work in 30 days, 50days, and 40 days respectively. if A is assisted by B on one day and by C on the next day alternatively, then find the time taken by them to finish the work? ​

Answer 1

Answer:

PART OF WORK ( FULL WORK ‘W’ ) DONE BY ‘A’ IN A DAY = (1/30)W

PART OF WORK ( FULL WORK ‘W’ ) DONE BY ‘B’ IN A DAY = (1/40)W

PART OF WORK ( FULL WORK ‘W’ ) DONE BY ‘C’ IN A DAY = (1/50)W

FOR THE FIRST THREE DAYS THE AMOUNT OF THE WORK DONE

= 3*(1/30) + 1/40 + 1/50 = (20+5+4)/200 = (29/200)W = 0.145W

IN 6x3 = 18 DAYS THE WORK COMPLETED = (6*29/200)W = (174/200)W

BALANCE OF WORK AT THE END OF 18 th DAY = (26/200)W = (13/100)W = 0.13W

WORK DONE BY ‘A’ ON 19 th DAY = (1/30)W = 0.03333W

WORK DONE BY ‘A’ ON 20 th DAY = 0.03333W

WORK STILL REMAINING ON 20 th DAY = ( 0.13–0.06666)W = 0.06334W

A,B AND C MUST WORK ON THE 21 st DAY PARTLY TO COMPLETE THIS PORTION OF WORK