A man can do a job in 15 days. His father takes 20 days and his son finishes it in 25 days. How long will they take to complete the job if they all work together?

The correct option is A Approximately 6.4 days

1 days’ work of a man $=\frac{1}{15}$

1 days’ work of father $=\frac{1}{20}$

1 days’ work of son $=\frac{1}{25}$

1 days’ work of all three persons = $(\frac{1}{15}+\frac{1}{20}+\frac{1}{25})=\frac{47}{300}$

$\begin{array}{cc}5& 15,20,25\\ 3& 3,4,5\\ 4& 1,4,5\\ 5& 1,1,5\\ & 1,1,1\end{array}$

$\therefore$ LCM $(15,20,25)=5\times 3\times 4\times 5=300$

So, all three together will complete the work in $\frac{300}{47}$ days $=6.4$ days.