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A company has two types of machines, Type R and Type S. Operating at a certain rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company uses the same number of each type of machine to do the job in 2 hours, how many machines of Type R were used?

Options: A. 3 B. 4 C. 6 D. 9 E. 12

Can anybody give me a quickest and simpler way to solve this? I took almost 3.5 min on this question to solve during a mock test. Still ended up guessing as I wasn't sure of the approach. Thanks.

Re: Work/Rate problem- A company has.. [#permalink]

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01 Jan 2017, 07:47

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baalok88 wrote:

A company has two types of machines, Type R and Type S. Operating at a certain rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company uses the same number of each type of machine to do the job in 2 hours, how many machines of Type R were used?

Options: A. 3 B. 4 C. 6 D. 9 E. 12

Can anybody give me a quickest and simpler way to solve this? I took almost 3.5 min on this question to solve during a mock test. Still ended up guessing as I wasn't sure of the approach. Thanks.

We are given rates of each machine and that the number of machines of each type being used is the same = x.

Re: A company has two types of machines, type R and type S [#permalink]

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18 Apr 2017, 06:05

Bunuel wrote:

enigma123 wrote:

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

A. 3 B. 4 C. 6 D. 9 E. 12

Rate of A - \(\frac{1}{36}\) job/hour, rate of x machines of A - \(\frac{1}{36}x\) job/hour; Rate of B - \(\frac{1}{18}\) job/hour, rate of x machines of B - \(\frac{1}{18}x\) job/hour, (same number of each type);

Remember that we can sum the rates, hence combined rate of A and B is \(\frac{1}{36}x+\frac{1}{18}x=\frac{3}{36}x=\frac{1}{12}x\) job/hour.

We are told that together equal number (x in our case) of machines A and B can do the job (1 job) in 2 hours --> \(Time*Rate=2*\frac{1}{12}x=1=Job\) --> \(x=6\).

Answer: C.

When I am double checking, why am I not getting the right answer? If 1 R machine is taking 36 hours, then 6 R machines will take 6 hours. If 1 S machine is taking 18 hours, then 6 S machines will take 3 hours. Together, they will take 6-3=3 hours.

Re: A company has two types of machines, type R and type S [#permalink]

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16 Aug 2017, 19:41

narendran1990 wrote:

Took 36 as the unit of work to be completed by R & S. [LCM of 36 & 18].

So, R does 1 unit per hour & S does 2 units per hour. Since an equal number of R & S machines have to be deployed, consider 'x' as the number of equipment. Additionally, the work is to be completed in 2 hours, so 18 units have to be manufactured.