A,B and C together can finish a task in 7.5 days. C is thrice as productive as A and B alone can do the task in 15 days. In how many days c…

- Let W denotes the whole given work.


- According to given data,



- (i) A, B & C together can complete the work W in 7.5 days.


- (ii) C is thrice as productive as A.


- (iii) B alone can complete the work W in 15 days. Hence,



- (iv) B alone in 1 day can complete the amount of work = W/15



- (v) Let D denotes the time (in days) in which A and C together can complete the work W.


- (vi) Let a & c denote the times (in days) in which A & C alone can complete the work W respectively. Hence,



- (vii) A & C alone in 1 day can complete the amounts of work W/a & W/c respectively.




- From (i), (iv) & (vii) we get following relation,



- 7.5*(W/a + W/15 + W/c) = W


- or 1/a + 1/15 + 1/c = 1/7.5 = 2/15


- or 1/a + 1/c = 1/15 …… (1a)



- From (ii) & (vii) we get following relation,



- W/c = 3*W/a or a = 3c …… (1b)



- From (1a) & (1b) we get,



- 1/3c + 1/c = 1/15


- or 4/3c = 1/15 or c = 20 (days) …… (1c)



- Hence from (1b) we get,



- a = 3c = 3*20 = 60 (days) …… (1d)



- Therefore from (v) & (vii) we get following relation,



- D*(W/a + W/c) = W


- or D*(1/a + 1/c) = 1


- or D*(1/60 + 1/20) = 1 [from (1c) & (1d)]


- or D/15 = 1 or D = 15 (days) [Ans]