X and Y, working together, can complete a work in 30 days, Y and Z, working together, can complete the same work in 40 days. and Z and X, working together, can complete the same work in 24 days. In how many days can X, Y and Z, working together, complete the work?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 20 days.
Total work (LCM of 30, 40, and 24) = 120 units
Efficiency of X and Y = 120/30 = 4 units/day
Efficiency of Z and Y = 120/40 = 3 units/day
Efficiency of Z and X = 120/24 = 5 units/day
Now, X + Y + Z + Y + Z + X = 12
⇒ 2 × (X + Y + Z) = 12
⇒ X + Y + Z = 6
Thus, X, Y, and Z do 6 units/day.
Hence, the required time taken = 120/6 = 20 days