Prahlad has done 1/3rd of a job in 30 days, Sarfaraz completes the rest of the job in 90 days. In how many days can they together do the job?

Let total work to be done = 90 units

Work done by Prahlad in 30 days = $$\frac{1}{3} \times 90 = 30$$ units

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

Remaining work = 90 - 30 = 60 units

Sarfaraz completes 60 units in 90 days

=> Sarfaraz's efficiency = $$\frac{60}{90} = \frac{2}{3}$$ units/day

(Prahlad + Sarfaraz)'s 1 day's work = $$1 + \frac{2}{3} = \frac{5}{3}$$ units/day

$$\therefore$$ Time taken by them together to do the job = $$\frac{90}{\frac{5}{3}}$$ 

= $$90 \times \frac{3}{5} = 54$$ days

=> Ans - (C)