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1. 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:

A. 3 days

B. 4 days

C. 4.5 days

D. 5.4 days

Solution:

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,

\begin{aligned} = \frac{1}{40} + \frac{1}{60} \\ = \frac{3 + 2}{120} \\ = \frac{5}{120} \\ = \frac{1}{24} \end{aligned}

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.

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