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
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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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