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two machines working together

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by jagdeep » Thu Jan 14, 2010 3:33 pm
It takes machine A x hours to manufacture a deck of cards that machine B can manufacture in y hours. If machine A operates alone for z hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously?

A) 100xy - z/
x + y


b) y(100x - z)/
x + y

c) 100y(x - z)/
x + y

d) x + y /
100xy - z

ans is B

e)

x + y - z/

100xy
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by ace_gre » Thu Jan 14, 2010 7:05 pm
Hi, here is my approach..

m/c A can complete 1 job(a deck of cards) in x hrs.
m/c A can complete 1/x job in 1 hr
m/c can complete z/x job in z hours.

Now remaining job = 100-z/x.

m/c B can complete 1 job in y hrs
therefore B can complete 1/y job in 1hr.

Time taken for both A and B working simultaneously to complete the remaining job
==> (100 - z/x) / (1/x +1/y)

Simplifying this, y(100x-z)/(x+y)
IMO B
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by jagdeep » Fri Jan 15, 2010 4:50 pm
Thanks a lot buddy

nice approach
ace_gre wrote:Hi, here is my approach..

m/c A can complete 1 job(a deck of cards) in x hrs.
m/c A can complete 1/x job in 1 hr
m/c can complete z/x job in z hours.

Now remaining job = 100-z/x.

m/c B can complete 1 job in y hrs
therefore B can complete 1/y job in 1hr.

Time taken for both A and B working simultaneously to complete the remaining job
==> (100 - z/x) / (1/x +1/y)

Simplifying this, y(100x-z)/(x+y)
IMO B
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