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A company has two types of machines, type R and type S

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

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New post 01 Jan 2017, 07:10
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.

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

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New post 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.

\(\frac{x}{36} + \frac{x}{18} = \frac{1}{2}\)

\(\frac{3x}{36} = \frac{1}{2}\)

\(6x = 36\)

\(x = 6\)

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

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New post 07 Jan 2017, 22:07
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Rate(R) = \(\frac{1}{36}\)
Rate(S) = \(\frac{1}{18}\)
Combined rate of both machines ,
Rate(RS)=Rate(R) + Rate(S) = \(\frac{1}{12}\)

we have given time , T = 2hrs , Workdone = 1 (for single job)
Plug in the values :

[Rate] * [Time] * [No. of machines] = Workdone

\(\frac{1}{12}\) * 2 * [No. of machines] = 1
[No. of machines] = 6

Ans : C

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

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New post 08 Jan 2017, 00:55
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Clearly R does 1/3 of the work and S does 2/3 of the work.
The time taken is 2 hours.

Number of machines of type R required are therefore , 36*(1/3)*(1/2)= 6

Similarly of S was asked it would have been , 18*(2/3)*(1/2)=6

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

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New post 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.

Please tell me where am I wrong :/

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

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New post 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.

Therefore, x+2x = 18, 3x = 18, x=6. [Correct Answer]



I was trying to solve using similar kind of method. But i could not understand how you arrived on 18? It will be great if you could elaborate.

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

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New post 09 Nov 2017, 22:26
There is no need to compute the combined rate in this case, explicitly that is.

Since the number of machines is the same, we can use a simple equation:

\(x*\frac{1}{36}+ x* \frac{1}{18} = \frac{1}{2}\) (here x machines work at the respective rates for 2 hours)

Solving for x, we get 6.
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A company has two types of machines, type R and type S   [#permalink] 09 Nov 2017, 22:26

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