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Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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29 Jan 2016, 03:20
3
18
00:00
A
B
C
D
E
Difficulty:
95% (hard)
Question Stats:
60% (03:11) correct 40% (04:00) wrong based on 131 sessions
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Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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29 Jan 2016, 10:20
1
2
Bunuel wrote:
Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
A. 46/9 B. 50/9 C. 50/11 D. 36/7 E. 210/41
Hi,
firstly it is a tough Q.. if one is clueless where to start, we can work on the info and easily eliminate three choices B,C, and D, and E too can be eliminated after a bit of thought...
IN first case A working for 6 days and B for 4 days, work is completed and in second case A for 4.5 days and B for 6 days, wk gets completed.. so if we combine A for 10.5 days and B for 10 , wk can be completed twice ... so wk to be completed once, A requires to work for 5.25 days and B for 5 days...
what can we make out ..
1) if both A and B work for 5 days, the work will not be completed, as we have to add .25 day work of B to it.. C (50/11)<5 is out...
2) work will be completed before (5+5.25)/2 days, as work of .25 days of A is being done by both together and A is faster than B.. so total time will be greater than 5.125 and should be less than 5.25, when A is faster than B .. so following can be eliminated A 46/9=5.111 <5.125 B 50/9=5.55>5.25
E 210/41= 5.122<5.125..
D 36/7=5.14...CORRECT .. between 5.125 and 5.25 is the answer..
answer can also be arrived at by proper work-time method. IN first case A working for 6 days and B for 4 days, work is completed or 6/a +4/b=1..(i)
and in second case A for 4.5 days and B for 6 days, wk gets completed.. so 4.5/a+ 6/b=1..(ii)
or 6/a +4/b= 4.5/a+ 6/b... we get a=3b/4 here .. substitute this value in (i).. 24/3b +4/b=1... this will give us b as 12.. so a= 3b/4=9..
we have to find 1/a+1/b as one day work of both.. 1/12 + 1/9= (3+4)/36= 7/36.. so time taken = 36/7 D
_________________
Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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31 Jan 2016, 08:27
Bunuel wrote:
Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
A. 46/9 B. 50/9 C. 50/11 D. 36/7 E. 210/41
hi Bunuel, THanks for such a lovely Q.. Edited
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Re: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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31 Jan 2016, 11:16
chetan2u wrote:
Bunuel wrote:
Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
A. 46/9 B. 50/9 C. 50/11 D. 36/7 E. 210/41
Hi,
firstly it is a tough Q.. if one is clueless where to start, we can work on the info and easily eliminate three choices B,C, and D, and E too can be eliminated after a bit of thought...
IN first case A working for 6 days and B for 4 days, work is completed and in second case A for 4 days and B for 13/2 days, wk gets completed.. so if we combine A for 10 days and B for 10 and 1/2 day, wk can be completed twice ... so wk to be completed once, A requires to work for 5 days and B for 5.25 days...
what can we make out ..
1) if both A and B work for 5 days, the work will not be completed, as we have to add .25 day work of B to it.. C (50/11)<5 is out...
2) work will be completed before (5+5.25)/2 days, as work of .25 days of B is being done by both together and A is faster than B.. so total time will be equal to 5.125 and should be less than 5.12, when A is faster than .. so following can be eliminated B 50/9=5.55>5.12 D 36/7=5.14>5.125 E 210/41= 5.122>5.12..
A 46/9=5.111 <5.12 is the answer..
answer can also be arrived at by proper work-time method. IN first case A working for 6 days and B for 4 days, work is completed or 6/a +4/b=1..(i)
and in second case A for 4 days and B for 13/2 days, wk gets completed.. so 4/a+ 6.5/b=1..(ii)
or 6/a +4/b= 4/a+ 6.5/b... we get a=4b/5 here ..E which the closest to the answer can be eliminated easily in POE when we know this relation substitute this value in (i).. 30/4b +4/b=1... this will give us b as 11.5.. so a= 4b/5=9.2..
we have to find 1/a+1/b as one day work of both.. 1/11.5 + 1/9.2= 20.7/105.8= 9/46.. so time taken = 46/9 A
The answer is given as D. I think you should check the highlighted part.
_________________
Re: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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31 Jan 2016, 15:51
2
2
A can complete 1/a of the task daily B can complete 1/b of the task daily
By the two statements (starting with A they complete the task in 10 days and starting with B they complete in 10,5 days), we have: I. 6/a + 4/b = 1 II. 6/b + 4,5/a = 1
Substituting it in the equation 1: 6/a + 4/(4a/3) = 1 => 6/a + 3/a = 1 => 9/a = 1 => a = 9 Substituting it in the equation III again: b = 4*9/3 => b = 12
Considering the values of A and B, they would be able to complete 1/9 + 1/12 = 7/36 of the task daily, so they would take 36/7 days to complete the task.
Re: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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31 Jan 2016, 19:36
Answer is (D) A does 1/a part in 1 day =2/a part in 2 days Similarly B does 2/b part is 2 days When A starts 2/a+2/b+2/a+2/b+2/a=1 => 6/a+4/b=1 .....................(1)
When B starts 2/b+2/a+2/b+2/a+2/b+1/2a(Half days work) =1 => 2/b=3/2a ..................(2)
Solving (1) and (2) we get a=9 and b = 12
A and B together does the work in ab/a+b =108/21 =36/7 days
Hence Answer is (D)
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Re: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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22 Feb 2016, 18:04
1
equation1: 6/a+4/b=1 equation2: 9/a+12/b=2 solving, a=9;b=12 let d=days for A and B to complete task working together d(1/9+1/12)=1 d(7/36)=1 d=36/7 days
Re: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days [#permalink]
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17 Mar 2016, 06:18
So I started and got the following equation, would love to get help on where I have gone wrong 6/a + 4/b = 1/10 That is 6 * 1/a (rate of A) and 4 * 1/b (rate of B) = 1/ 10 (overall time utilised)
second equation followed the same route, is my equation wrong??
Re: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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17 Mar 2016, 07:53
3
1
Bunuel wrote:
Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
A. 46/9 B. 50/9 C. 50/11 D. 36/7 E. 210/41
When A starts, A works for 6 days and B for 4 days to complete the work. 6/a + 4/b = 1 Work
When B starts, A works for 4.5 days and B for 6 days to complete the work. 4.5/a + 6/b = 1 Work
Solving these two equations simultaneously, we get: 18/a + 12/b = 3 9/a + 12/b = 2 9/a = 1 a = 9 b = 12
Rate of work while working together = 1/9 + 1/12 = 7/36 Time taken to complete the work = 36/7 days Answer (D)
_________________
Re: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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17 Mar 2016, 09:15
1
Bunuel wrote:
Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
A. 46/9 B. 50/9 C. 50/11 D. 36/7 E. 210/41
Let their efficiency ratio be a:b Therefore, 6*a+4*b=4.5*a+6*b =>a to b is 4:3 Number of days taken will be 3*k and 4*k, where k is a constant. If they work together they take (3*k)*(4*k)/3*k+4*k = 12*k^2/7*k = 12*k/7 Look at the option. Only D could be the correct one.
Re: Working alone, A can complete a task in ‘a’ days and B in ‘b’ days. Th [#permalink]
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05 May 2018, 02:31
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