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If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to

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Bunuel
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If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to [#permalink] New post  24 Sep 2023, 11:47
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If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to complete a job, how many minutes will it take for 6 Machine A's and 15 Machine B's working together to complete the same job?

A. 66 minutes
B. 76 minutes
C. 96 minutes
D. 106 minutes
E. 120 minutes

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gmatophobia
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If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to [#permalink] New post  24 Sep 2023, 12:08
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Bunuel wrote:
If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to complete a job, how many minutes will it take for 6 Machine A's and 15 Machine B's working together to complete the same job?

A. 66 minutes
B. 76 minutes
C. 96 minutes
D. 106 minutes
E. 120 minutes


If 8 Machine A's take 3 hours to complete the work, 1 Machine A will take 8 times the time.

  • Time taken by 1 Machine A to complete the task = 3 * 8 = 24 hours

If 10 Machine B's take 4 hours to complete the work, 1 Machine B will take 10 times the time.

  • Time taken by 1 Machine B to complete the task = 10 * 4 = 40 hours

Let's assume that the task is LCM(24,40) = 120 units

  • Work done by 1 Machine A in 1 hour (rate of Machine A) = 120/24 = 5 units
  • Work done by 1 Machine B in 1 hour (rate of Machine B) = 120/40 = 3 units

  • Work done by 6 Machine A's in 1 hour = 6 * 5 = 30 units
  • Work done by 15 Machine B's in 1 hour = 15 * 5 = 45 units

Total work done by 6 Machine A's + 15 Machine B's in 1 hour = 30 +45 = 75 units

Time taken to complete the work = \(\frac{120 }{ 75} = (1 + \frac{45}{75}\)) hours

Time in minutes = \(60(1 + \frac{45}{75}) = 60 + (9*4) = 60 + 36 = 96\) minutes

Option C
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JeffTargetTestPrep
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Re: If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to [#permalink] New post  24 Sep 2023, 12:17
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Bunuel wrote:
If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to complete a job, how many minutes will it take for 6 Machine A's and 15 Machine B's working together to complete the same job?

A. 66 minutes
B. 76 minutes
C. 96 minutes
D. 106 minutes
E. 120 minutes


8 Machines A:

Time = 3 hours
Work = 1 job
Rate = Work/Time = 1/3 job/hour

Rate of 1 Machine A = (1/8)(1/3) = 1/24 job/hour

10 Machines B:

Time = 4 hours
Work = 1 job
Rate = Work/Time = 1/4 job/hour

Rate of 1 Machine B = (1/10)(1/4) = 1/40 job/hour

6 Machines A and 15 Machines B together:

Rate = 6(1/24) + 15(1/40) = 25/40 = 5/8 job/hour
Work = 1 job
Time = Work/Rate = 1/(5/8) = 8/5 hours

8/5 hours = (8/5) × 60 = 96 minutes

Answer: C
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SaquibHGMATWhiz
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Re: If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to [#permalink] New post  25 Sep 2023, 00:35
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Bunuel wrote:
If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to complete a job, how many minutes will it take for 6 Machine A's and 15 Machine B's working together to complete the same job?

A. 66 minutes
B. 76 minutes
C. 96 minutes
D. 106 minutes
E. 120 minutes


Solution:

  • Let us assume the work be 12

  • 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to complete a job
Attachment:
wnrt.png
wnrt.png [ 16.07 KiB | Viewed 653 times ]

  • 6 machine As will have rate \(6\times \frac{1}{2}=3\)
  • And 15 machine Bs will have rate \(=15\times \frac{3}{10}= 4.5\)
  • Total rate \(=3+4.5=7.5\)
Attachment:
wnrt2.png
wnrt2.png [ 11.9 KiB | Viewed 637 times ]



Hence the right answer is Option C
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Abhishek009
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Re: If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to [#permalink] New post  25 Sep 2023, 07:20
Bunuel wrote:
If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to complete a job, how many minutes will it take for 6 Machine A's and 15 Machine B's working together to complete the same job?

A. 66 minutes
B. 76 minutes
C. 96 minutes
D. 106 minutes
E. 120 minutes

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\(8*a_e*3 = 10*4*b_e= 120\) (120 = Total work)

SO, \(a_e = 5\) & \(b_e = 3\) {\(_e\) represents efficiencies of respective machines}

Quote:
how many minutes will it take for 6 Machine A's and 15 Machine B's working together to complete the same job?


\(\frac{120}{(6*5)+(15*3)}*60 = 96\), Answer must be (C)
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Re: If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to [#permalink]
25 Sep 2023, 07:20
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