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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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Joined: 18 Dec 2017
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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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22 Feb 2020, 18:44
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Question Stats:

38% (02:50) correct 62% (02:38) wrong based on 42 sessions

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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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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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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

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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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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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Joined: 30 Jun 2019
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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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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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Joined: 04 Jan 2015
Posts: 3337
Re: A can do a piece of work in 24 days and A and B together can-do same  [#permalink]

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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.

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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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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.

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
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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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