Question

2 men can do a piece of work in 6 hours and 4 hours respectively after the first has worked for 2 hours,he is joined by other. by when should the work be completed

Answer 1

Let us say A can do the work in 6 hours. So A can do (1/6)th of the work in 1 hour.

B can do the same work in 4 hours. So B can do (1/4)th of the work in 1 hour.

If A work for 2 hours, he has done (2/6) or (1/3)rd of the work and what remains is (2/3)rd of the work.

A and B together do (1/6)+(1/4)

= (4+6)/(4x6)

= (10/24) or (5/12)th of the work in 1 hour.

So to do the remaining (2/3) of the work, A and B will take

(2/3)/(5/12)

= (2*12)/(3*5)

=24/15 or (8/5) or 1.6hours.

So the entire work will get done in 2 + 1.6 = 3.6 hours from the start of the work by A.