A work can be completed by P and Q in 12 days, Q and R in 15 days, R and P in 20 days. In how many days P alone can finish the work ?

Let efficiency of P,Q and R to finish the work be $$p , q , r$$ units/day respectively

Let total work to be done = 60 units

P and Q complete the work in 12 days

=> Efficiency of P and Q = $$p + q = \frac{60}{12} = 5$$

Similarly, $$q + r = 4$$ ----------(i)

$$r + p = 3$$

Adding the three equations, we get :

=> $$2 (p + q + r) = 5 + 4 + 3 = 12$$

=> $$p + q + r = \frac{12}{2} = 6$$

From eqn(i), => $$p + 4 = 6$$

=> $$p = 6 - 4 = 2$$ units/day

$$\therefore$$ Time taken by P to finish the work alone = $$\frac{60}{2} = 30$$ days