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Bunuel
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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 07 Apr 2020, 05:02
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C
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67% (02:38) correct 33% (03:02) wrong based on 240 sessions

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Annie alone can do a job in 20 days while Bob alone can do it in 40 days. Annie starts the job, and after 3 days, Ben joins her. Again, after a few more days, Cathy joins them and they together finish the job. If Cathy has done 10% of the job, then in how many days was the job done?

A. 15
B. 14
C. 13
D. 12
E. 11

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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 07 Apr 2020, 05:41
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Bunuel
Annie alone can do a job in 20 days while Bob alone can do it in 40 days. Annie starts the job, and after 3 days, Ben joins her. Again, after a few more days, Cathy joins them and they together finish the job. If Cathy has done 10% of the job, then in how many days was the job done?

A. 15
B. 14
C. 13
D. 12
E. 11
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Annie starts the job, and works alone for 3 days, so work done by her = 3/20

Cathy has done 10% of the job, so A and B do the remaining work that is 90% of the work.

Out of this 90% or \(\frac{9}{10}\) work, A has already done \(\frac{3}{20}\) by herself,, so A and B do \(\frac{9}{10}-\frac{3}{20}=\frac{15}{20}=\frac{3}{4}^{th}\) work together.

A and B can do \(\frac{1}{20}+\frac{1}{40}\) or \(\frac{3}{40}\) in one day, so they will do \(\frac{3}{4}\) work in \(\frac{\frac{3}{4}}{\frac{3}{40}}=\frac{3*40}{3*4}=10\) days.

As A has worked throughout and he works for 3+10=13 days, the answer is 13 days

C
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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 07 Apr 2020, 05:56
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Bunuel
Annie alone can do a job in 20 days while Bob alone can do it in 40 days. Annie starts the job, and after 3 days, Ben joins her. Again, after a few more days, Cathy joins them and they together finish the job. If Cathy has done 10% of the job, then in how many days was the job done?

A. 15
B. 14
C. 13
D. 12
E. 11
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Please find below the video solution of the problem

Answer: Option C

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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 07 Apr 2020, 06:03
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Ta=20, Tb=40=2Ta
We know that Annie worked for 3 days before Ben joined.
Hence after 3 days the fraction of work left is \(\frac{17}{20}\)
Let the days that Annie and Ben worked together alone be \(x\).
Then after x days, the fraction of the work left is \(\frac{17}{20}-\frac{3}{40}x = \frac{34-3x}{40}\)
Let the days that Annie, Ben and Cathy worked together be \(y\) while the days taken by Cathy alone to do the work be \(Tc\).
Then \(\frac{3}{40}y+\frac{y}{Tc}=\frac{34-3x}{40}\)
But we know that Cathy alone does a tenth of the work. Hence \(\frac{y}{Tc}=\frac{1}{10}\)
Therefore \(\frac{3}{40}y+\frac{1}{10}=\frac{34-3x}{40}\)
\(\frac{3}{4}y+1=\frac{34-3x}{4}\)
\(3y+4=34-3x\)
\(3y+3x=30\)
hence \(x+y=10\)
But Annie already worked for \(3 days\),
so total days taken to complete the work \(= 10+3=13days\)

The answer is C.
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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 07 Apr 2020, 06:05
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Solution:


    Let’s assume total work as LCM(20,40)
      Total work = LCM(20, 40) = 40 units
    Rate of Annie = \(\frac{40}{20} = 2\) units per day
    Rate of Bob = \(\frac{40}{40} = 1\) units per day
      Combined rate of Annie and Bob = \(2 + 1 = 3\) units per day
      Work done by Cathy = \(\frac{10}{100}*40 = 4\) units
      Work done by Annie in first three days = \(3*2 = 6\) units
      Work left = \(40 – 4-6 = 30\) units
        Number of days when Annie and Bob worked together = \(\frac{30}{3} = 10\) days
    Total number of days = \(10 + 3 = 13\) days
    We are not adding the number of days when Cathy worked, because that's already counted while finding the number of days they worked combined
Answer: Option C
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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 07 Apr 2020, 06:28
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Let total job =40 M days
A's efficiency = 2 M days/ day
B's efficiency = 1 M day / day
C's efficiency = x M day / day
Now,
2x + (x-3) = 36
Where x is the total number of days for which work has been done
x =13 days
Option C is the answer

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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 07 Apr 2020, 07:01
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rate of A= 1/20
and in rate of B =1/40
in 3 days A has done ; 1/20 * 3 ; 3/20 of work
together A & B rate= 1/20 +1/40 ; 3/40
and given that C has done 10% of job meaning the work done by A & B is 90% or say 9/10th of work
we have total work done by A &B ; 9/10 - 3/20 ; 15/20 ; 3/4 work done by A &B
so total time taken by A&B ; 3/4 *40/3 ; 10 days
so total work days would be 10 days + 3 days ; 13 days
OPTION C :

Bunuel
Annie alone can do a job in 20 days while Bob alone can do it in 40 days. Annie starts the job, and after 3 days, Ben joins her. Again, after a few more days, Cathy joins them and they together finish the job. If Cathy has done 10% of the job, then in how many days was the job done?

A. 15
B. 14
C. 13
D. 12
E. 11

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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 15 Apr 2020, 07:01
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Answer is C option- 13 days

Now it is given , Annie take 20 days and Bob take 40 days

LCM= 40, therefore work= 40 units

Rate of A= 40/20= 2 unit/ day

Rate of Ben= 40/40=1 unit/day

Now In start A works for 3 days alone, 3*2= 6 units done

C did 10% of work, that is 10% of 40= 4 units

Remaining work, 40-( 6+ 4) = 30 units

A+B= 2+1= 3 units/ day

Therefore, 30/3= 10 days

Total no of days= 3+ 10= 13 days.

C joins A and B at the last and they together finish the work, so obviously C joins A and B on the last day.

So, don't think about the no of days for C.
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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 19 Jul 2020, 10:41
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Annie alone can do a job in 20 days while Bob alone can do it in 40 days. Annie starts the job, and after 3 days, Ben joins her. Again, after a few more days, Cathy joins them and they together finish the job. If Cathy has done 10% of the job, then in how many days was the job done?

A. 15
B. 14
C. 13
D. 12
E. 11

Solution:

We see that A’s rate is 1/20 and B’s rate is 1/40. Since C completed 10% of the job, A and B together completed 90% of the job. Since A works on the job every day, we can let a = the number of days A works on the job and create the equation:

a/20 + (a - 3)/40 = 9/10

Multiplying the equation by 40, we have:

2a + a - 3 = 36

3a = 39

a = 13

Answer: C
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Annie alone can do a job in 20 days while Bob alone can do it in 40 da 20 Jul 2025, 01:01
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