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