Annie alone can do a job in 20 days while Bob alone can do it in 40 da

Question

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

Are You Up For the Challenge: 700 Level Questions

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

Are You Up For the Challenge: 700 Level Questions

chetan2u · Accepted Answer

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

GMATinsight · Answer

Please find below the video solution of the problem

Answer: Option C

https://www.youtube.com/watch?v=L2C8Vod05Zo

eakabuah · Answer

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.

Enchanting · Answer

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

gurmukh · Answer

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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Archit3110 · Answer

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 :

thenikhilseth · Answer

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.

ScottTargetTestPrep · Answer

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

Are You Up For the Challenge: 700 Level Questions

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

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Annie alone can do a job in 20 days while Bob alone can do it in 40 da

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