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 the total work be \(48\) units.
Let Amar do \(m\) work, Akbar do \(k\) work, and Anthony do \(n\) units of work in a month.
Amar and Akbar complete the project in \(12\) months.
Hence, in a month they do \(\frac {48}{12}=4\) units of work.
\(⇒m+k = 4\)   ……… (i)
Similarly,
\(k+n = 3\)       ……….. (ii)
and \(m+n = 2\)     ……… (iii)
On solving these equations,
\(m=\frac 32\)

\(k=\frac 52\)

\(n=\frac 12\)
Here, Amar works neither the fastest not the slowest and he does 1.5 units of work in a month.
Hence, to complete the work, time taken,
\(=\frac {48}{1.5}\)

\(= 32\) months

So, the answer is \(32\) months.