A and B can do a piece of work together in 10 days, B and C can do the same work together in 15 days, while C and A can do the same work together in 20 days. In how many days can A, B and C do the same work, working together?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 120/13
Concept Used :
Total work = Efficiency × Number of days
Given :
A and B can do a piece of work together in 10 days
B and C can do the work together in 15 days,
C and A can do the work together in 20 days
Now let the total work done is LCM of (10, 15, 20) = 60 units
Efficiency of A and B = 60/10 = 6 units/day ....(i)
Efficiency of B and C = 60/15 = 4 units/day ....(ii)
Efficiency of A and C = 60/20 = 3 units/day ....(iii)
Now, adding equations (i), (ii) and (iii)
⇒ 2(A + B + C) = 13
⇒ (A + B + C) = 13/2
Now the time taken by (A + B + C) to complete the work together
⇒ 60/(13/2) = 120/13.
Hence the work is completed by (A + B + C) together in 120/13 days.