Working 5 hours a day, A can Complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in:

Solution (By Examveda Team)

1^st Method:
Working 5 hours a day, A can complete the work in 8 days i.e.
= 5 × 8 = 40 hours
Working 6 hours a day, B can complete the work in 10 days i.e.
= 6 × 10 = 60 hours
(A + B)'s 1 hour's work,
$$\eqalign{ & = \frac{1}{{40}} + \frac{1}{{60}} \cr & = \frac{{3 + 2}}{{120}} \cr & = \frac{5}{{120}} \cr & = \frac{1}{{24}} \cr} $$
Hence, A and B can complete the work in 24 hours i.e. they require 3 days to complete the work.

2^nd Method:
% 1 hour's work of A = $$\frac{{100}}{{40}}$$ = 2.5%
% 1 hour's work of B = $$\frac{{100}}{{60}}$$ = 1.66%
(A + B) one hour's % work,
= (2.5 + 1.66) = 4.16%
Time to complete the work,
= $$\frac{{100}}{{4.16}}$$ = 24 hours
Then, $$\frac{{24}}{8}$$ = 3 days
They need 3 days, working 8 hours a day to complete the work.