solving method for puzzle

[rednewguy]

there are 3 persons A,B,C.
A does the job in X days.
B does the same job in Y days
C does the same job in Z days.
A+B+C all together in P days
now the question is
A initially performs some part of the job for J days
B then continues for K days.
How many days will it take for C to finish the remaining job left by A and B.

can u give any generic methods to solve questions of this type.

thanks

 

[paereap]

Erm what does the line about A+B+C can do it for P days? The quantity P seems to be unecessary in solving the problem here.

 

[newelltech]

If we assume that X,Y,Z,J,K are all given, then we can solve it without knowing P. (PaereaP saidias thisiht tooot )

Rate for A is 1/X ( he does 1/X of the job in a day) jobs/day
Rate for B is 1/Y jobs/day
Rate for C is 1/Z jobs/day

A works for J days: J/X jobs (days times jobs per day)
B works for K days: K/Y jobs
C works for Q days: Q/Z

They're going to do one job so
J/X+K/Y+Q/Z = 1 and we can solve for Q

If only J and K are known, there is not enough information to determine Q because we only have 2 equations and 4 unknowns.

If only X,Y and Z are given then there is not enough information to determine Q because we only have 2 equations and 3 unknowns.

Are you sure you didn't leave something out?

 

[paereap]

Actually I've seen quite a few of these questions around, and most of the time X, Y, Z, J and K are given, so there should be no worry. But basically the "algorithm" to solving this kinda problems is just to find the rate of the workers (1/X, 1/Y and 1/Z), multiply it by the number of days (J/X, K/Y), then add them up to form an equation. Just to summarise what newelltech said, yeah.