Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is
Explanation:
Let the total work to be done = LCM (12, 16, 24) = 48 units.
Let the efficiency of Amar, Akbar and Anthony be ‘x’, ‘y’ and ‘z’ units/month
⇒ x + y = 48/12 = 4 …(2) ⇒ y + z = 48/16 = 3 …(1) ⇒ z + x = 48/24 = 2 …(3)
Adding all these equations ⇒ x + y + z = 9/2 = 4.5 …(4)
Solving these four equations we get, x = 1.5, y = 2.5 and z = 0.5
∴ The person who is neither slowest not fastest is Amar with efficiency of 1.5 units/month.
∴ Time required by Amar to complete the task alone = 48/1.5 = 32 months.
Hence, 32.
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