Question

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

Answer 1

Let's denote the rates of work of Amar, Akbar, and Anthony as A, B, and C units/year, respectively.

From the given data:

1. Amar and Akbar together can complete the project in 1 year. $A + B = 1$ (1)

2. Akbar and Anthony together can complete the project in 16 months (or 4/3 years). $B + C = 3/4$ (2)

3. Anthony and Amar together can complete the project in 2 years. $C + A = 1/2$ (3)

Adding all three equations, we get: 2(A + B + C) = 1 + 3/4 + 1/2 2(A + B + C) = 9/4 A + B + C = 9/8

From equation (1), we get: A = 1 - B

Plugging this into $A + B + C = 9/8$:

1 - B + B + C = 9/8

1 + C = 9/8

C = 1/8

From equation (2):

B = 3/4 - 1/8 = 5/8

Now, let's identify the worker who is neither the fastest nor the slowest:

A = 1 - 5/8 = 3/8

B = 5/8

C = 1/8

Clearly, Akbar (B) is neither the fastest nor the slowest

If he works alone, he will take:

Time = Total work/Rate = 1 / (5/8) = 8/5 years = 19.2 months.

So, Akbar will take approximately 19.2 months to complete the project on his own