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

Question

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

GMATWhizTeam · Accepted Answer

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 .

GMATinsight · Answer

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

newyork2012 · Answer

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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fireagablast · Answer

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?

EgmatQuantExpert · Answer

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

globaldesi · 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
Can you please help where did I miss

Kinshook · Answer

@TheNightKingGiven: A can do a piece of work in 24 days and A and B together can-do same piece of work in 16 days.
Asked: Find out in how many days B can complete 2 times more work if B work with 50% more efficiency?
Let us assume that B takes x days to complete the work alone

1/24 + 1/x = 1/16
1/x = 1/16 - 1/24 = 1/48
x = 48 days

With 50% more efficiency, B will take 48*2/3 = 32 days to complete the work alone
B will take 32*3 = 96 days to complete 2 times more work iwth 50% more efficiency.

IMO D

Lord_Biplab · Answer

Two times more work means 200% + 100% = 300 % of work, i.e. 3 times of original work.

shivani1351 · Answer

This is a kind of trap question, but if you pay close attention to the framing, it will be smooth sailing.
We know: Rate of work done = Work done/Time taken

Let the work done by 'W'.

So, A = W/24 and A+B = W/16 (where A and B represent the Rate of Work done by A and B respectively)

In such questions, take the Work done (W) = LCM (Time taken by A, Time taken by B) = LCM (24,16) = 48

Thus, A = 2 and A+B = 3, rendering B = 1.

Now, we need to find out in how many days B can complete  2 times more work  (and not two times the work), i.e. 2*W+W = 3W = 144

Number of days required by B to complete 144 units of work with 50% more efficiency = (144)/(1*1.5) = 96 days

Hence, the correct option is Option (D) 96 days (Answer)

sujoykrdatta · Answer

We can assume the work to be the least common multiple of 24 and 16 (for ease of calculations) = 48 units
=> Rate of doing work of A = 48/24 = 2 units per day
Rate of doing work of A and B = 48/16 = 3 units per day
=> Rate of doing work of B = 3 - 2 = 1 units per day

B has to complete two times more work, i.e. 48 + 48 x 2 = 48 + 96 = 144 units at 50% higher rate i.e. 1.5 units per day
=> Time = Work/Rate = 144/1.5 = 144/(3/2) = 144 x (2/3) = 96 days

Answer D

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

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