Word problem

[Aman verma]

Q: B,V and M are three friends with different productivity. B working alone needs as much time as V and M together, while V himself needs 8 hours more working alone than when he works with M. B working alone needs 8 hours less than V needs working alone. In how much time B,V and M working together can complete the job ?

a) 4

b) 5

c) 6

d) 7

e) 8

OA [spoiler]c)[/spoiler]

PS: Please solve this algebraically

[cans]

B,V,M working together... B = V and M working together. Thus answer is B/2 (Half of time taken by B)
B = V-8 and V = 8 + VM/(V+M) = 8+B (which we already know)
B = VM/(V+M). (we have 2 equations and 3 variables)
I think question needs some correction.

[Aman verma]

B,V,M working together... B = V and M working together. Thus answer is B/2 (Half of time taken by B)
B = V-8 and V = 8 + VM/(V+M) = 8+B (which we already know)
B = VM/(V+M). (we have 2 equations and 3 variables)
I think question needs some correction.

As I have mentioned, it is trully tough to solve algebraically, however by plugging the option it can be easily solved. Even I have tried my best but unable to reach an algebraical solution to this one. The question is correct, allright !

[cans]

what I am saying is that we have 2 equations and 3 variables. Thus all the options should fit.
Lets take E. 8. it means time taken by B = 16.
thus by V = B + 8 = 24
thus 24 = 8 + (24m)/(24+m) -> 2(24+m) = 3m or m=48.
This also gives the solution and is correct.