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# Sam can repair a machine in 15 days and Ross can repair in 25 days

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Manager
Joined: 03 Feb 2017
Posts: 74
Location: Australia
GMAT 1: 720 Q48 V40
Sam can repair a machine in 15 days and Ross can repair in 25 days  [#permalink]

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24 Jun 2017, 03:02
1
9
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:08) correct 34% (02:33) wrong based on 156 sessions

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Sam can repair a machine in 15 days and Ross can repair the same machine in 25 days. If they decide to repair the machine on alternate days, with Ross on the first day, followed by Sam on the second day and so on till the repair is completed, how many days do they take to complete the repair work.

A) 17
B) 18
C) 19
D) 20
E) 21
Senior Manager
Joined: 28 Jun 2015
Posts: 286
Concentration: Finance
GPA: 3.5
Re: Sam can repair a machine in 15 days and Ross can repair in 25 days  [#permalink]

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24 Jun 2017, 04:08
5
1
1
Work done by Sam in one day = 1/15, in Ross = 1/25.
Total work done by Sam in the first day and Ross in the second day = 1/15 + 1/25 = 8/75.

No. of days to complete the work: n(8/75) = 1
n = 75/8 = 9.375.

So, it will take 9.375 two day's work, hence 9.375 * 2 = ~19 days.
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Joined: 02 Sep 2009
Posts: 56300
Re: Sam can repair a machine in 15 days and Ross can repair in 25 days  [#permalink]

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24 Jun 2017, 06:49
1
danlew wrote:
Sam can repair a machine in 15 days and Ross can repair the same machine in 25 days. If they decide to repair the machine on alternate days, with Ross on the first day, followed by Sam on the second day and so on till the repair is completed, how many days do they take to complete the repair work.

A) 17
B) 18
C) 19
D) 20
E) 21

Use LCM:
Portion of the work done by Sam is 1/15 = 5/75;
Portion of the work done by Ross is 1/25 = 3/75.

Together in 2*9 = 18 days they'll do (5 + 3)*9 = 72 parts out of 75. On the 19th day Sam will do the remaining job. So, the answer is 19.

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Re: Sam can repair a machine in 15 days and Ross can repair in 25 days  [#permalink]

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26 Oct 2018, 03:27
Together in 2*9 = 18 days they'll do (5 + 3)*9 = 72 parts out of 75. On the 19th day Sam will do the remaining job. So, the answer is 19.

Can someone explain this part?
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Re: Sam can repair a machine in 15 days and Ross can repair in 25 days  [#permalink]

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26 Oct 2018, 07:59
1
danlew wrote:
Sam can repair a machine in 15 days and Ross can repair the same machine in 25 days. If they decide to repair the machine on alternate days, with Ross on the first day, followed by Sam on the second day and so on till the repair is completed, how many days do they take to complete the repair work.

A) 17
B) 18
C) 19
D) 20
E) 21

Let the total work be 75 units.

Efficiency of Sam = 5 units/day
Efficiency of Ross = 3 units/day

Since they work alone on alternate days then they complete 8 units of work in 2 days..

That is they complete 72 units of work in 18 days (Simply multiply by 9)

After that 3 units of work is left which Ross completes in 1 days...

So, the work will be completed in 19 days, Answer must be (C) 19 days
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Manager
Joined: 14 Jun 2018
Posts: 222
Re: Sam can repair a machine in 15 days and Ross can repair in 25 days  [#permalink]

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26 Oct 2018, 12:52
Sam does 100/15% or 6.67% work in 1 day
Ross does 100/25 or 4% work in 1 day
Total work done in 2 days = 6.67+4 = 10.67% work
10.67 * 9 = 96% work in 18 days
remaining 4% done in the 19th day
Re: Sam can repair a machine in 15 days and Ross can repair in 25 days   [#permalink] 26 Oct 2018, 12:52
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