A₁​, A_2​, and A₃​, alone can complete a piece of work in 12 hours, 24 hours and 16 hours respectively. Working together, in how much time they will complete the same work?

5 Hours 20 Minutes

A₁ 1 hour work = \(\frac{1}{12}\) 

A₂ 1 hour work = \(\frac{1}{24}\) 

A₃ 1 hour work = \(\frac{1}{16}\) 

Together, their 1 hour = \(\frac{1}{12}\)  + \(\frac{1}{24}\)  + \(\frac{1}{16}\)  = \(\frac{3}{16}\) 

When they work together, they will do the job in \(\frac{16}{3}\) hours = 5 hours 20 minutes