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A can do a piece of work in 24 days and A and B together can-do same

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A can do a piece of work in 24 days and A and B together can-do same  [#permalink]

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New post 22 Feb 2020, 18:44
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A can do a piece of work in 24 days and A and B together can-do same piece of work in 16 days. Find out in how many days B can complete 2 times more work if B work with 50% more efficiency?
(a) 68 days
(b) 90 days
(c) 80 days
(d) 96 days
(e) 72 days

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Re: A can do a piece of work in 24 days and A and B together can-do same  [#permalink]

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New post 25 Feb 2020, 04:22
TheNightKing wrote:
A can do a piece of work in 24 days and A and B together can-do same piece of work in 16 days. Find out in how many days B can complete 2 times more work if B work with 50% more efficiency?
(a) 68 days
(b) 90 days
(c) 80 days
(d) 96 days
(e) 72 days


Solution:


    • Let \(A\), and \(B\) be the rate of work done by A and B per day, respectively.
    • Let the total work be \(LCM(24, 16) = 48\) units.
      o \(A = \frac{(total\ work)}{time} =\) \(\frac{48}{24} = 2\)
      o \(A + B = \frac{(total\ work)}{time} =\) \(\frac{48}{16}= 3\)
         \(A + B = 3\)
         \(2 + B = 3\)
         \(B = 1\).
    • B is working at rate of \(1\) unit per day.
      o Total work to be done by \(B =48+2*48 = 144\)
      o New rate of work of B = \(1 + \frac{50}{100}*1 = 1.5\)
      o Time taken = \(\frac{work }{ rate} = \frac{144}{1.5} = 96\) days.
Hence, the correct answer is Option D.
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Re: A can do a piece of work in 24 days and A and B together can-do same  [#permalink]

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New post 25 Feb 2020, 08:30
TheNightKing wrote:
A can do a piece of work in 24 days and A and B together can-do same piece of work in 16 days. Find out in how many days B can complete 2 times more work if B work with 50% more efficiency?
(a) 68 days
(b) 90 days
(c) 80 days
(d) 96 days
(e) 72 days


Let, work units = Any multiple of (24, 16) = 48

i.e. A's work unit done in one day = 48/24 = 2 units
i.e. (A+B)'s work unit done in one day = 48/16 = 3 units

i.e. B's work unit done in one day = 3-2 = 1 units

i.e. B's will do 2*48 i.e. 96 units in = 96/1 = 96 days

Answer: Option D
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Re: A can do a piece of work in 24 days and A and B together can-do same  [#permalink]

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New post 25 Feb 2020, 20:33
A can do a piece of work in 24 days and A and B together can-do same piece of work in 16 days.

It takes b 16 days to complete what a can do in 8 days ... so it will take b 48 days to finish the whole thing

If b work with 50% more efficiency ...48/1.5=32 days to finish the work

To finish 3 ....32*3=96

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Re: A can do a piece of work in 24 days and A and B together can-do same  [#permalink]

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New post 27 Feb 2020, 13:30
I'm confused how "2 times more work" somehow translates to 3 days of work.
If B takes 48 days to do the the work, it would take 96 days to do 2x the work.

it takes B 48 days to do the work.
50% more efficiency = 48/1.5 = 32

2 = 1/32 *t
64 = t

Why is "two times more work" equal to 3?
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Re: A can do a piece of work in 24 days and A and B together can-do same  [#permalink]

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New post 28 Feb 2020, 10:52

Solution



Given
    • A can do a piece of work in 24 days.
    • A and B together can-do same piece of work in 16 days

To find
    • In how many days B can complete 2 times more work if B work with 50% more efficiency

Approach and Working out
    • In 24 days, A is completing the work.
    o So, in 16 days, A will complete 16/24 or 2/3 of work.
    o Thus, 1/3 of work is completed by B in 16 days.

In 16 days, A is doing 2/3 of word and in same number of days, B is doing 1/3rd of work.
    • So, A’s efficiency is half of A.
    • Hence, B will complete the same work in twice the time i.e. in 48 days.
      o So, 2 times more work will be complete in 48*3 days.
      o If B’s efficiency is increased by 50% then work will be done in 96/1.5 time.
         =96 days.

Hence, option d is the correct answer.

Correct Answer: Option d
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Re: A can do a piece of work in 24 days and A and B together can-do same  [#permalink]

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New post 29 Feb 2020, 05:13
EgmatQuantExpert wrote:

Solution



Given
    • A can do a piece of work in 24 days.
    • A and B together can-do same piece of work in 16 days

To find
    • In how many days B can complete 2 times more work if B work with 50% more efficiency

Approach and Working out
    • In 24 days, A is completing the work.
    o So, in 16 days, A will complete 16/24 or 2/3 of work.
    o Thus, 1/3 of work is completed by B in 16 days.

In 16 days, A is doing 2/3 of word and in same number of days, B is doing 1/3rd of work.
    • So, A’s efficiency is half of A.
    • Hence, B will complete the same work in twice the time i.e. in 48 days.
      o So, 2 times more work will be complete in 48*3 days.
      o If B’s efficiency is increased by 50% then work will be done in 96/1.5 time.
         =96 days.

Hence, option d is the correct answer.

Correct Answer: Option d

Hey Payal
Can you please explain this segment
Hence, B will complete the same work in twice the time i.e. in 48 days.
So, 2 times more work will be complete in 48*3 days.
o If B’s efficiency is increased by 50% then work will be done in 96/1.5 time.
=96 days.
As per my understanding
B can finish with improved efficiency the same work in 32 days
so to do the work that is twice he should have taken 32*2 = 64 days
Can you please help where did I miss
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Re: A can do a piece of work in 24 days and A and B together can-do same   [#permalink] 29 Feb 2020, 05:13
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