Prabodh has done 1/2 of a job in 30 days, Sapan completes the rest of the job in 45 days. In how many days can they together do the job?

Let total work to be done = 60 units

Prabodh has done 1/2 of a job i.e. $$\frac{60}{2} = 30$$ units in 30 days

=> Prabodh's efficiency = $$\frac{30}{30} = 1$$ unit/day

Work left = 60 - 30 = 30 units which is done by Sapan in 45 days

=> Sapan's efficiency = $$\frac{30}{45} = \frac{2}{3}$$ units/day

Prabodh and Sapan 1 day's work = $$1 + \frac{2}{3} = \frac{5}{3}$$ units/day

$$\therefore$$ Time taken by them together to complete the work = $$60 \div \frac{5}{3}$$

= $$60 \times \frac{3}{5} = 12 \times 3 = 36$$ days