enigma123 wrote:
Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?
A) (x – y)/(x + y)
B) x/(y – x)
C) (x + y)/(xy)
D) y/(x – y)
E) y/(x + y)
Given: Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours.
Asked: If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete because of A's help?
Work done by Machine A & Machine B together in 1 hours
1/x + 1/y = x+y/xy
Total hours needed to finish the work = xy/(x+y)
Ratio of work done by Machine A to work done by Machine B = 1/x : 1/y = y:x
the fraction of the job that B will not have to complete because of A's help = Machine A's contribution to the job = y/(x+y) * 1
IMO E
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com