P takes 10 days and Q takes 24 days to complete a work. With the help of R, they all work together and finish it in 6 days. Find the payment they receive out of a total remuneration of Rs.1000.

P = 10 days

Q= 24 days

P+Q+R = 6 days

Total work = lcm (10,24,6)= 120 days

P's effiency = $$120\div10$$ =12

Q's effiency = $$120\div24$$ =5

(P+Q+R)'s effiency = $$120\div6$$ = 20

to find out R's effi = (P+Q+R)'s effiency -P's effiency-Q's effiency = 20 -12-5 = 3

P'wage = $$\frac{tot wage}{tot effi}P's effiency$$

            $$\frac{1000}{20}12= 600 Rs$$

Q'wage = $$\frac{tot wage}{tot effi}Q's effiency$$

$$\frac{1000}{20}5= 250 Rs$$

R'wage = $$\frac{tot wage}{tot effi}R's effiency$$

$$\frac{1000}{20}3= 150 Rs$$