P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

5$ \dfrac{5}{11} $

5$ \dfrac{6}{11} $

6$ \dfrac{5}{11} $

6$ \dfrac{6}{11} $

Explanation:

P can complete the work in $\left(12 \times 8\right)$ hrs. = 96 hrs.

Q can complete the work in $\left(8 \times 10\right)$ hrs. = 80 hrs.

$\therefore$ Ps1 hours work =$ \dfrac{1}{96} $and Qs 1 hours work =$ \dfrac{1}{80} $.

$\left(P + Q\right)$s 1 hours work =$ \left(\dfrac{1}{96} +\dfrac{1}{80} \right) $=$ \dfrac{11}{480} $.

So, both P and Q will finish the work in$ \left(\dfrac{480}{11} \right) $hrs.

$\therefore$ Number of days of 8 hours each =$ \left(\dfrac{480}{11} \times\dfrac{1}{8} \right) $=$ \dfrac{60}{11} $days = 5$ \dfrac{5}{11} $days.