Question

A and B can separately finish a piece of work in 20 and 15 days respectively.they worked together for 6 days after which B was replaced by C.if the work was finished in next 4 days then the number of days C alone could do the work is.

Answer 1

Let the no of days C could do the work alone be x days
So in 1 day he works=1/x part
So in 4days he worked=4/x part
A will do alone in one day=1/20part
B will do alone in one day=1/15 part
Part of work done by A and B together in 6 days
6/20+6/15=(18+24)/60
=42/60=7/10
Remaining work=3/10 part of total work
Remaining work is completed by A and C in 4 days so
4/20+4/x=3/10
4/x=3/10-2/10
4/x=1/10
x=40 days