# 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 Answer: Option A
1st 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, $\begin{array}{l} =\frac{1}{40}+\frac{1}{60} \\ =\frac{3+2}{120} \\ =\frac{5}{120} \\ =\frac{1}{24} \end{array}$ Hence, A and B can complete the work in 24 hours i.e. they require 3 days to complete the work.
2nd 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, $=\frac{100}{4.16}=24 \text { hours }$ Then, $\frac{24}{8}=3 \text { days }$ They need 3 days, working 8 hours a day to complete the work.