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Bunuel
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When they work alone, B needs 25% more time to finish a job than A does 03 Apr 2020, 06:29
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When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

A. 22
B. 20
C. 18
D. 16
E. 14


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B
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When they work alone, B needs 25% more time to finish a job than A does 04 Apr 2020, 00:22
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Bunuel
When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

A. 22
B. 20
C. 18
D. 16
E. 14


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Solution


    • Let us assume that the time taken by B to complete the job be \(b\) days.
      o Then time taken by A to complete the job = \(\frac{b}{1.25}\) days \(= \frac{4b}{5}\) days.
         Then time taken by A to complete the half of the job \(= \frac{2b}{5} \)days
      o Also, time taken by B to complete 5% of the job \(= b*\frac{5}{100} = \frac{b}{20}\) days
    • According to the questions,
      o \(\frac{2b}{5} + 4 + \frac{b}{20} = 13\)
      \(⟹\frac{(8b + b)}{20} = 9\)
      \(⟹9b = 9*20\)
      \(⟹b = 20\)
Thus, the correct answer is Option B.
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When they work alone, B needs 25% more time to finish a job than A does 03 Apr 2020, 14:41
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Suppose A needs '16a' days to complete the job and B needs '20a'.

Number of days needed by A to complete half of the job = 8a

Number of days needed by B to complete 5% of the job= \(\frac{20a}{20}=a\)

8a+4+a = 13

a=1

B alone finish the entire job in 20 days


Bunuel
When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

A. 22
B. 20
C. 18
D. 16
E. 14


Are You Up For the Challenge: 700 Level Questions
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When they work alone, B needs 25% more time to finish a job than A does 03 Apr 2020, 17:03
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B needs 25% more time than A
So, if Time taken by A = 4x days, Time taken by B = 5x days
A does half the work, So A works alone for 2x days --- (1)
A and B work for 4 days --- (2)
B works alone for 5x/20 = x/4 days ---(3)
therefore, 2x + 4 + x/4 = 13
or, x= 4
So, B alone can do the work in 5 × 4 = 20 days

correct answer is B
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When they work alone, B needs 25% more time to finish a job than A does 04 Apr 2020, 13:22
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1/2-0.05 = (A+B)4
45/100 = (5/4B+B)4
45/100 = (9/4B)4
9/20 = 9B
1/20 = B

20 days for B alone (and 16 days for A alone)
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When they work alone, B needs 25% more time to finish a job than A does 18 May 2024, 03:55
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Apologies for the format, however I would like to post my way of solving this question.

The rate of A is 1/a and the rate of B is 1/1.25a. Using a common denominator of 5 you get rate of A is 5/5a and rate of B is 4/5a. The question tells us that A did 50% of the job, and when A and B were done working together after 4 days only 5% of the work was left to do. This tell us that the rate of A and B together is 45% of the job / 4 days. In other words 45/100 * 1/4 which is 45/400. This can be rewritten as 9/80. Using 5/5a and 4/5a we get that the combined rate is 9/5a. Therefore, 5a = 80 and a = 16. B takes 25% longer and 25% of 16 is 4 therefore B takes 20 days.
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When they work alone, B needs 25% more time to finish a job than A does 17 Jun 2024, 15:47
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50% done by A alone 1st; 5% done by b alone at last. In total 55% work done. Now, this means (A+B) does 45% work in 4 days => 100% work will be done by (A+B) in 80/9 days (by unitary method).

Let A take t time to complete the whole work alone. Then
1/t + 1/1.25t = 1/ (80/9)
=> t = 16
=> 1.25 t = 20 days . (Answer)
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When they work alone, B needs 25% more time to finish a job than A does 25 Jun 2024, 04:02
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Bunuel
When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

A. 22
B. 20
C. 18
D. 16
E. 14


Are You Up For the Challenge: 700 Level Questions

Solution


    • Let us assume that the time taken by B to complete the job be \(b\) days.
      o Then time taken by A to complete the job = \(\frac{b}{1.25}\) days \(= \frac{4b}{5}\) days.
         Then time taken by A to complete the half of the job \(= \frac{2b}{5} \)days
      o Also, time taken by B to complete 5% of the job \(= b*\frac{5}{100} = \frac{b}{20}\) days
    • According to the questions,
      o \(\frac{2b}{5} + 4 + \frac{b}{20} = 13\)
      \(⟹\frac{(8b + b)}{20} = 9\)
      \(⟹9b = 9*20\)
      \(⟹b = 20\)
Thus, the correct answer is Option B.
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How time taken by A is b/1.25?
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When they work alone, B needs 25% more time to finish a job than A does 25 Jun 2024, 06:49
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Let time taken for A alone to complete the job be x then B's time will be 1.25x


A and B work for 4 days

1/x + 1/1.25x = w/4

w = 9/1.25x


1/2 + 9/1.25x + 1/20 = 1

x = 16

So time taken for B alone to do the job = 1.25 x 16 = 20

Answer B

Adewale Fasipe, GMAT quant instructor from Lagos Nigeria.­
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When they work alone, B needs 25% more time to finish a job than A does 29 Jun 2025, 08:39
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