P and Q undertook to do a work for Rs 7200. P alone could do it in 20 days and Q alone in 12 days. With the assistance of R they finished the work in 5 days. What is the share (in Rs) of R?

Let total work to be done = L.C.M (20,12) = 60 units

P alone could do this work in 20 days, => P's efficiency = $$\frac{60}{20}=3$$ units/day

Similarly, Q's efficiency = $$\frac{60}{12}=5$$ units/day

Let R's 1 day's work = $$r$$ units/day

According to ques,

=> $$5(3+5+r)=60$$

=> $$8+r=\frac{60}{5}=12$$

=> $$r=12-8=4$$

Now, ratio of efficiencies of P, Q and R = $$3:5:4$$

=> R's share in total amount of Rs. 7200 = $$\frac{4}{(3+5+4)}\times7200$$

= $$4\times600=Rs.$$ $$2400$$

=> Ans - (B)