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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


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 26th Jan, 2024

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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