Ram can do a piece of work in 3 days. Shyam can do 3 times the same work in 8 days, and Rohit can do 5 times the same work in 12 days. If a working day is 6 hours long, how much time will the three take to complete the work together?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5 hrs 20 min
Turn each statement into work done per day: doing 3 works in 8 days means \(\frac{3}{8}\) of a work per day. A day here is 6 working hours, so the per-day rate is shared over 6 hours.
Ram \(=\frac{1}{3}\), Shyam \(=\frac{3}{8}\), Rohit \(=\frac{5}{12}\) of the work per day
Together \(\displaystyle =\frac{8}{24}+\frac{9}{24}+\frac{10}{24}=\frac{27}{24}=\frac{9}{8}\) of the work per day
Per hour \(\displaystyle =\frac{9}{8}\div6=\frac{3}{16}\) of the work
Time \(\displaystyle =\frac{16}{3}\) hours \(=5\frac{1}{3}\) hours \(=5\) hrs 20 min