Question : A1, A2, and A3 alone can complete a piece of work in 12 hours, 24 hours, and 16 hours respectively. Working together, in how much time will they complete the same work?
Option 1: 5 hours 30 minutes
Option 2: 5 hours 20 minutes
Option 3: 4 hours 20 minutes
Option 4: 3 hours 30 minutes
Correct Answer: 5 hours 20 minutes
Solution :
Time taken by A
1
to do the work = 12 hours
⇒ 1 day's work of A
1
= $\frac{1}{12}$
Time taken by A
2
to do the work = 24 hours
⇒ 1 day's work of A
2
= $\frac{1}{24}$
Time taken by A
3
to do the work = 16 hours
⇒ 1 day's work of A
3
= $\frac{1}{16}$
If A
1
, A
2
, and A
3
work together, work will be done in a day
= $\frac{1}{12}$ + $\frac{1}{24}$ + $\frac{1}{16}$
= $\frac{4+2+3}{48}$
= $\frac{9}{48}$
= $\frac{3}{16}$
So, Time taken by A
1
, A
2
, and A
3
together to do the work
= $\frac{16}{3}$
= $5\frac{1}{3}$ hours
= 5 hours 20 minutes
Hence, the correct answer is 5 hours 20 minutes.
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