A, B, C and D, working separately, can do a piece of work in 5 days, 6 days, 8 days and 10 days, respectively. In how many days can A and B complete the work together, if they are assisted by C and D on alternate days, starting with C?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 2days.
Work rates (per day):
A = 1/5 , B = 1/6 , C = 1/8 , D = 1/10
Work done on odd days (A + B + C) = 1/5 + 1/6 + 1/8 = (24 + 20 + 15) / 120 = 59/120
Work done on even days (A + B + D) = 1/5 + 1/6 + 1/10 = (12 + 10 + 6) / 30 = 28/60 = 14/30 = 7/15
Work done in 2 days = 59/120 + 7/15 = 59/120 + 56/120 = 115/120 = 23/24
Remaining work after 2 days = 1 - 23/24 = 1/24
On 3rd day (A + B + C) work = 59/120 > 1/24
So, total days = 2 + (remaining work)/(work on 3rd day)
= 2 + (1/24) / (59/120)
= 2 + (1/24) × (120/59)
= 2 + 5/59 ≈ 2.085 days = 2 days