If P, Q and R can complete a job in 24, 16 and 12 days respectively, how long will they take to complete the job working together?

Let n be the time required to complete the work in days.

Time required by P = 24 days ==> Efficiency of P = 1/24

Time required by Q = 16 days ==> Efficiency of P = 1/16

Time required by P = 12 days ==> Efficiency of P = 1/12

Time x Efficiency = Work 

$$ n ( \frac{1}{24} + \frac{1}{16} + \frac{1}{12} ) = 1 $$

$$ \frac{1}{n} = \frac{ 2 + 3 + 4}{48} = \frac{3}{16} $$

i.e n = 16 / 3 = 5 days, 8hrs

Therefore, Option D is correct.