A certain number of pages need to be typed. A, B and C are assigned to

Question

A certain number of pages need to be typed. A, B and C are assigned to do this job. However, C leaves after 4 days when 40% of the job was complete. In this way, it takes 13 days to finish the job. Also, B can type twice as fast as A. How much would the fastest worker take to type the entire set of pages alone?

A. 22.5 days
B. 45 days
C. 30 days
D. 20 days
E. 40 days

A. 22.5 days
B. 45 days
C. 30 days
D. 20 days
E. 40 days

rajatchopra1994 · Accepted Answer

Explanation: A and B take 9 days to complete the remaining 100% - 40%=60% of the job. In one day A and B can complete – 60/9=20/3% of the job Since A is twice as slow as B, A completes 1/3 of job. Hence, A can finish= 20/3 × 1/3 = 20/9% of the job in a day ....(1) Since B is twice as fast as A, B completes 2/3 of job. Hence, B can finish = 20/3 × 2/3 = 40/9% of the job in a day ....(2) In the first 4 days. A and B would have finished = 20/3 × 4= 80/3% of the job Therefore, C would have finished = 40-80/3 = 40/3% of the job in 4 days So, C can finis h = 40/3 ÷ 4 = 10/3% of the job ....(3) Hence, B is the fastest among the three workers. Now B will take 9/40 × 100 days = 22.5 days. IMO-A

Please give kudos, If you find the explanation Good Enough

nick1816 · Answer

A, B and C can finish 40% of the work in 4.days; hence, they can finish 100% of work in 10 days

A and B can finish 60% of work in 9 days; hence, both can finish 100% of work in 15 days

Suppose total work= lcm(10,15)=30

A+B+C= 30/10=3.....(1)

A+B= 30/15=2.....(2)

Also, B=2A.......(3)

From (1), (2) and (3)

C=1, B= 4/3 and A= 2/3

Time taken by B to type the entire set alone= 30/(4/3)= 22.5 days

chetan2u · Answer

So from 4th to 13th day A and B finish 60% of the work. That is, in 13-4 or 9 days 60% of the work or 100*9/60 or 15 days for 100% work.

Ratio of days taken by A and B = A:B=2:1, so 2/3 work is by B or B does 2/3 in 15 days, that is, B does entire work in 15*3/2 or 22.5 days.
Now A takes double the time, so 22.5*2=45 days.

What about C?
 A logical and quick way  - C's 4 days work results in 2 days combined work of A and B, as the combined work goes down by 2 days from 15 to 13 with the help of C's 4 days work.
So C is somewhere between A and B. 
We can straight way mark 22.5 days as the answer.
OR 
 solve for C 
A and B can work  4*\frac{1}{15}=\frac{4}{15}  in 4 days, but with the help of C, they have done 40/100 or 2/5 work in 4 days..
So C's 4 days work =  \frac{2}{5}-\frac{4}{15}=\frac{6-4}{15}=\frac{2}{15} 
Therefore, C's one day work =  \frac{1}{4}*\frac{2}{15}=\frac{2}{60}=\frac{1}{30}  or C will do entire work in 30 days

A

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