X can do a work in 3 days, Y does three times work in 8 days, and Z does five times the same work in 12 days. If they have to work together for 6 hours in a day, then in how much time can they complete the work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 5 hours 20 minutes
Total working hours of X in 3 days = 6 × 3 = 18 hours
The total working hours of Y in 8 days = 6 × 8 = 48 hours
Total working hour of Z in 12 days = 6 × 12 = 72 hours
Y does three times work and Z does five times work.
So, Y can finish one unit of work = 48/3 = 16 hours
And Z can finish one unit of work = 72/5 hours
Take the LCM of 18, 16, and 72/5 = 144
Efficiency of X = 144/16 = 9
⇒ Y = 144/18 = 8
⇒ Z = 144/(72/5) = 10
So, total time taken by them = = 144/27 = = 5 hours 20 min