Indian Institute of Foreign Trade 2009 Solved Paper

Amount of work done by A in one week $=\frac{1}{6}$
Amount of work done by V in one week $=\frac{1}{9}$
Amount of work done by Y in one week $=\frac{1}{12}$
Therefore Amount of work done by A, V and Y in one week $=\frac{1}{6}+\frac{1}{9}+\frac{1}{12}=\frac{13}{36}$
They work together for 2 weeks therefore work done in these 2 weeks is $=\frac{26}{36}$
Amount of work remaining is $1-\frac{26}{36}=\frac{10}{36}$
Amount of work done by V and Y in one week$=\frac{1}{9}+\frac{1}{132}=\frac{7}{36}$
If total number of weeks required to complete the work is n then only V and Y work together for $\left(\mathit{n}-3\right)$ weeks
Therefore work done in these (n-3) weeks is $=\frac{7\times \left(\mathit{n}-3\right)}{36}$
Remaining $\frac{10}{36}-\frac{7\times \left(\mathit{n}-3\right)}{36}$ is completed by Y in one week
Therefore $\frac{10}{36}-\frac{7\times \left(\mathit{n}-3\right)}{36}=\frac{1}{12}$
Solving we get n = 4
Therefore The job would be completed in 4 weeks
Therefore our answer is option 'A'