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# Two machines are sawing wood but due to space limitations only one at

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Joined: 02 Sep 2009
Posts: 58427
Two machines are sawing wood but due to space limitations only one at  [#permalink]

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08 Feb 2019, 03:12
00:00

Difficulty:

45% (medium)

Question Stats:

63% (03:11) correct 37% (02:51) wrong based on 38 sessions

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Two machines are sawing wood but due to space limitations only one at a time can operate. Machine A is used for the first shift and the other machine for the second shift, while both work half of the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with current work schedule?

A. 14

B. 13

C. 11

D. 9

E. 7

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Two machines are sawing wood but due to space limitations only one at  [#permalink]

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Updated on: 09 Feb 2019, 00:39
1
Bunuel wrote:
Two machines are sawing wood but due to space limitations only one at a time can operate. Machine A is used for the first shift and the other machine for the second shift, while both work half of the third shift. Machine A can do the job in 12 days if it worked two shifts and Machine B can do the job in 15 days if it worked two shifts. How many days will it take to do the job with current work schedule?

A. 14

B. 13

C. 11

D. 9

E. 7

given rate of A = 1/12 for two days so per day = 1/24 ; half day 1/48
and rate of B = 1/15 for two days , so per day = 1/30; half day 1/60

(1/24 + 1/30) + (1/48 + 1/60) = 80/9 days =
9
IMO D

Originally posted by Archit3110 on 08 Feb 2019, 07:13.
Last edited by Archit3110 on 09 Feb 2019, 00:39, edited 1 time in total.
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Re: Two machines are sawing wood but due to space limitations only one at  [#permalink]

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08 Feb 2019, 12:30
A 12 days if 2 shifts, 24 days if 1 shift, 48 days if half shift
B 15 days if 2 shifts, 30 days if 1 shift, 60 days if half shift

(1/24 + 1/30) + (1/48 + 1/60) = 80/9 days = ~9d
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Re: Two machines are sawing wood but due to space limitations only one at  [#permalink]

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08 Feb 2019, 14:05
Machine A:

Time = 2 shifts of 8 hours each* 12 days= 16*12 hrs to finish work alone.

Rate A= 1/(16*12)

Similarly, Rate B= 1/(16*15)

Rate A+B= 27/(16*15*12)
Time to finish, working together = x days*12 hours a day= 12x

As T=1/r, we have
12x=(16*15*12)/27= 80/9=~9 days

Ans D

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Re: Two machines are sawing wood but due to space limitations only one at  [#permalink]

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08 Feb 2019, 14:57
A 1/24 of task per shift; also does half of one shift-> 1/48 during the half shift
B: 1/30 of task per shift; also does half of one shift -> 1/60 during the half shift

total of A work in the 1.5 shift - 1/24 +1/48 = 1/16
total of B work in the 1.5 shift - 1/30 +1/60 = 1/20

Work formula: T=W/R
1/ (1/16 +1/20) = 80/9
Approx 9 days.
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Re: Two machines are sawing wood but due to space limitations only one at  [#permalink]

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09 Feb 2019, 04:42
Bunuel

Let's assume the total units of work to be done is 60. Therefore W = 60

A = 60/12
= 5 Units / Day for two shifts

Therefore Machine A does 2.5 units / day - shift

B = 60/15
= 4 Units / Day for two shifts

Therefore Machine B does 2 units / day - shift

Now if A works first shift, B works second shift and both work half of third shift, then the total units of work on a day
= 2.5 + 2 + 2.5 + 2
= 9 Units / Day

Therefore, total number of days required is
= 60/9
= 6.66
~ 7 Days (Answer E)

Can you help me understand where I am going wrong?
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Two machines are sawing wood but due to space limitations only one at  [#permalink]

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09 Feb 2019, 05:16
pikolo2510 wrote:
Let's assume the total units of work to be done is 60. Therefore W = 60

A = 60/12
= 5 Units / Day for two shifts

Therefore Machine A does 2.5 units / day - shift

B = 60/15
= 4 Units / Day for two shifts

Therefore Machine B does 2 units / day - shift

Now if A works first shift, B works second shift and both work half of third shift, then the total units of work on a day
= 2.5 + 2 + 2.5 + 2
= 9 Units / Day

Therefore, total number of days required is
= 60/9
= 6.66
~ 7 Days (Answer E)

Can you help me understand where I am going wrong?

Hi pikolo2510.

Look at highlighted portions above.

Great method. Just have to be careful in your execution.
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Two machines are sawing wood but due to space limitations only one at   [#permalink] 09 Feb 2019, 05:16
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