Working alone, B needs 50% more time to complete a certain job than A

Question

Working alone, B needs 50% more time to complete a certain job than A does. A and B completes the same job in 15 days in the following manner: A works alone till half the job is done, then A and B work together for 2 days, and finally B works alone to complete the remaining 10% of the job. In how many days can B alone complete the entire job ?

A. 16
B. 20
C. 24
D. 30
E. 36

A. 16
B. 20
C. 24
D. 30
E. 36

chetan2u · Accepted Answer

So, we know that B takes 50% more time..
 If A does it in A days, B will take 1.5A days...

A and B completes the same job in 15 days in the following manner:
1) A works alone till half the job is done,......  so time taken is   \frac{A}{2} 
2) then A and B work together for 2 days,.....  so time taken is 2 days 
3) and finally B works alone to complete the remaining 10% of the job, .....  as B days for 100%, so   \frac{B}{10} days = \frac{1.5A}{10} 
Adding all three  \frac{A}{2}+2+\frac{1.5A}{10}=15......\frac{6.5A}{10}=15-2=13....A=\frac{13*10}{6.5}=20 .
A is 20, and, thus, B becomes 1.5*20=30.

D

Sumitgupta85 · Answer

I tried to solve it through different ways.
B takes 50% more time means ratio of efficiency of A to B is 3:2.
Now 50/3x+2+10/2x =15
Solving it, we get x= 10/6
Efficiency of B =20/6
Time taken by B to complete entire work =100*6/20=30 days.

But
When I tried to equate 40% of work done in 2 days to efficiency i got wrong answer.
40/5x=2.
Kindly help

Posted from my mobile device

TestPrepUnlimited · Answer

It looks like a flawed question to me. According to the 15-day procedure, we can deduce that A and B working together for 2 days should complete 40% of the task. From here we calculate that the rate of A is 12% per day and B is 8% per day. 1/8% = none of the answer choices.

ShaikhMoice · Answer

Sir just 1 question though
considering 20 & 30 days in 2 days they are doing 33.33 % work whereas as mentioned in the question they complete 40 % work in 2 days.
Kindly guide what i am missing here.
TIA.

adewale223 · Answer

From the question, if time taken for A to complete task is x, then B will take 1.5x.

Now since time and rate are inversely proportional, rate of A will be 1.5x

B will be x.

Therefore time taken for A to do half of work = 1/3x

Since 10% of work will be left for B, time taken by B will be 1/10x.

So

1/3x + 2 + 1/10x = 15

1/3x + 1/10x = 13

x = 13/390

Remember x is the rate of B.

Now time it will take for B alone to complete job

T = 1/13/390

Which gives 390/13

= 30 days

GMAT quant instructor Lagos

Posted from my mobile device

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Working alone, B needs 50% more time to complete a certain job than A

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