Prabhat has done 1/2 of a job in 12 days. Santosh completes the rest of the job in 6 days. In how many days can they together do the job?

Let total work to be done = 24 units

Prabhat has done 1/2 of a job i.e. $$\frac{24}{2} = 12$$ units in 12 days

=> Prabhat's efficiency = $$\frac{12}{12} = 1$$ unit/day

Work left = 24 - 12 = 12 units which is done by Santosh in 6 days

=> Santosh's efficiency = $$\frac{12}{6} = 2$$ units/day

Prabhat and Santosh 1 day's work = 1 + 2 = 3 units/day

$$\therefore$$ Time taken by them together to complete the work = $$\frac{24}{3} = 8$$ days