work problems

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taichka123: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Oct 15, 2008 7:18 pm

by taichka123 » Fri Oct 17, 2008 8:31 pm

Please help me with these two problems

1)
A and B can complete stitching in 6 hours, B and C can do the same in 8 hours, while C and A can complete it in 12 hours. How long would each of them take, doing the same work, separately?

A) A=48, B=9.6, C=16
B) 9.6, 48, 16
C) 16, 9.6, 48
D) 16, 48, 9.6

2) 1/4 of a work is completed by 8 persons in 12 days. Find the number of persons required to complete the remaining work in 16 days.

A)2
B)3
C)4
D)1

Thank you!

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Source: Beat The GMAT — Problem Solving | Fri Oct 17, 2008 8:31 pm

2009wish: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Sep 13, 2008 10:33 pm

by 2009wish » Fri Oct 17, 2008 10:08 pm

1.

work done by A+B in one day will be 1/ 6. similarly it will be 1/ 8 and 1/ 12 for B+C & C+A.

Adiing the above equation we get.........

2( A+B+C) =1 /6 +1/ 8+ 1/ 12

so work done by A+B+C in one day will be =3/ 16

3/ 16 -1/6 =work done by C in one day ie......48 ; A is 16

C is the answer

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Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

Re: work problems

by Morgoth » Fri Oct 17, 2008 10:28 pm

taichka123 wrote:
2) 1/4 of a work is completed by 8 persons in 12 days. Find the number of persons required to complete the remaining work in 16 days.

A)2
B)3
C)4
D)1

Are you sure about the answer choices.

if 8 people finish 1/4 job in 12 days, you would definitely need more than 8 to finish the remaining job i.e 3/4 in 16 days.

Let me know if I am missing something.

I am getting 18 as the answer.

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Fri Oct 17, 2008 10:30 pm

1) I get C) as the answer

Rate*time*no of machines = work

Let R1 be A's rate,R2 be B's rate and R3 be C's rate

(R1+R2)*6*1 = 1 => R1 = 1/6 - R2 (1)

(R2+R3) *8*1 = 1 =>R3 = 1/8 - R2 (2)

(R3+R1)*12*1 = 1 (3)

Substituting (1) and (2) in (3)

(1/8-R2+1/6-R2)*12*1 = 1

R2 = 5/48 SO T2 = 48/5 = 9.6

Substitute R2' values in (1) and (2)
R1=16
R3=48

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Fri Oct 17, 2008 10:33 pm

For (2)

I did

1/4*8*12 = 3/4*x*16

x= 2

Morgoth, thougts?

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Morgoth: Master | Next Rank: 500 Posts; Posts: 316; Joined: Mon Sep 22, 2008 12:04 amFollowed by: 1 member; Thanked: 36 times

by Morgoth » Fri Oct 17, 2008 11:27 pm

cramya wrote:For (2)

I did

1/4*8*12 = 3/4*x*16

x= 2

Morgoth, thougts?

I am not sure about what you did.

Here is how I am getting 18

people * rate * time = work

8 * rate * 12 = 1/4

rate = 1/( 4*8*12)

people * rate * time = work

people * 1/( 4*8*12) * 16 = 3/4

people = 3/4 * ( 4*8*12)/16 = 18.

Alternatively, look at it in this way

let total work be 80

8 workers complete 20 out of 80 work in 12 hours.

do you think 2 workers can complete remaining 60 out of 80 in just 16 hours.

Let me know your thoughts.

Thanks.

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2009wish: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Sep 13, 2008 10:33 pm

by 2009wish » Fri Oct 17, 2008 11:34 pm

agree with morgoth ------- work is directly proportional to men , days keeping the other constant.

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raunekk: Legendary Member; Posts: 1159; Joined: Wed Apr 16, 2008 10:35 pm; Thanked: 56 times

by raunekk » Sat Oct 18, 2008 1:25 am

@cramya

i think d question shud b..
2)
1/4 of a work is completed by 8 persons in 12 days. Find the number of additional persons required to complete the remaining work in 16 days.

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4meonly: Legendary Member; Posts: 891; Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member; Thanked: 27 times; GMAT Score:660(

by 4meonly » Sat Oct 18, 2008 3:13 am

cramya wrote:1) I get C) as the answer

Rate*time*no of machines = work

Let R1 be A's rate,R2 be B's rate and R3 be C's rate

(R1+R2)*6*1 = 1 => R1 = 1/6 - R2 (1)

(R2+R3) *8*1 = 1 =>R3 = 1/8 - R2 (2)

(R3+R1)*12*1 = 1 (3)

Substituting (1) and (2) in (3)

(1/8-R2+1/6-R2)*12*1 = 1

R2 = 5/48 SO T2 = 48/5 = 9.6

Substitute R2' values in (1) and (2)
R1=16
R3=48

Super!

I had another approach:
What can be cocnluded from the main statement?
A and B can complete stitching in 6 hours, B and C can do the same in 8 hours, while C and A can complete it in 12 hours.
I think it clearly shoes that the rates can be arranged in incresing order in such manner: B>A>C
so time can be arranged in C>A>B. The only answer that fits this is
C) 16, 9.6, 48

Answer without any calculations

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taichka123: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Wed Oct 15, 2008 7:18 pm

Re: work problems

by taichka123 » Sat Oct 18, 2008 6:11 am

Morgoth wrote:
taichka123 wrote:
2) 1/4 of a work is completed by 8 persons in 12 days. Find the number of persons required to complete the remaining work in 16 days.

A)2
B)3
C)4
D)1
Are you sure about the answer choices.

if 8 people finish 1/4 job in 12 days, you would definitely need more than 8 to finish the remaining job i.e 3/4 in 16 days.

Let me know if I am missing something.

I am getting 18 as the answer.

The answer to the first question is indeed C)
The answer to the second problem is 2 people. ?

Thank you for all of your help!

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