A and B can complete a piece of work in 120 days, B and C can complete it in 150 days, and A and C can complete it in 200 days. In how many days can B alone complete two-fifths of the same work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 80.
A and B can complete a piece of work in 120 days.
B and C can complete it in 150 days.
A and C can complete it in 200 days.
Total work = Work done per day × Total time taken
LCM (120, 150, 200) = 600
Let the total work be the LCM of the time taken by different workers.
So, total work = 600 units
Let the efficiencies of A, B, and C be denoted by A, B, and C.
According to the question -
A + B = 600/120
A + B = 5 ....(1
B + C = 600/150
B + C = 4 ....(2
A + C = 600/200
A + C = 3 ....(3
(1) + (2) + (3) -
A + B + B + C + A + C = 5 + 4 + 3
2(A + B + C) = 12
(A + B + C) = 12/2
(A + B + C) = 6 ....(4
(4) - (3) -
(A + B + C) - (A + C) = 6 - 3
A + B + C - A - C = 3
B = 3
Now, the time taken by B to complete two-fifths of the same work = (600/3) × (2/5) = 80 days
In 80 days B can alone complete two-fifths of the same work.