Alex takes 6 days to complete a work, while Bill takes 10 days to comp

Question

Alex takes 6 days to complete a work, while Bill takes 10 days to complete the work alone. Charles takes 15 days to complete the work alone. All of them work together for 2 days. Then Alex and Bill quit. How many days more will it take Charles to do the remaining work alone?

A. 7
B. 9
C. 5
D. 10
E. 2

There are two ways to solve this question.

Method 1 involves using equations
Method 2 involves ratios and percentages.

Method 2 is faster and is logic based. Even if you have a non math background you can crack it.

Remember GMAT math tests you on mathematical reasoning.
If you need help in math. Ping me. I`m happy to help

Solution for the above problem here: https://letsgmat.blogspot.com/2020/08/g ... lls-5.html

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Show Answer

Official Answer

C

ZucchiniGMAT · Answer

The way I solved the problem was relatively simple and quick.

To complete a project it takes each person the following amount of time:

Alex = 6 days 
Bill = 10 days 
Charles = 15 days

If working alone each person completes this fraction of the project each day. I provided the fractions with the least common denominator.

Alex = 1/6 = 5/30
Bill = 1/10 = 3/30
Charles = 1/15 = 2/30

If they all work together for two days then 2 * ( 5/30 + 3/30 + 2/30 ) = 20/30 and 10/30 of the project remains. Charles completes 2/30 of the project by himself so it will take him 5 days to finish 10/30 of the project.

Answer: C

Hope this helps!

CrackverbalGMAT · Answer

Another method to do this is to take the LCM(6,10,15) = 60 units done by each in their respective time.

Alex does 60 units in 6 days. In 1 day he does 10 units of work.

Bill does 60 units in 10 days. In 1 day he does 6 units of work.

Charles does 60 units in 15 days. In 1 day he does 4 units of work.

All working together, complete 10 + 6 + 4 = 20 units in 1 day.

Therefore in 2 days, work done = 40 units.

Work remaining = 60 - 40 = 20 units

Since Charles does 4 units of work in 1 day, 20 units will take  \frac{20}{4}  = 5 days

Option C

Arun Kumar

SarangArvind · Answer

Alex can do the work in 6 days. Work done by him in 1 day = 1/6
Bill can do the work in 10 days. Work done by him in 1 day = 1/10
Charles can do the work in 15 days. Work done by him in 1 day = 1/15

Total work done by all three of them in 1 day = 1/6 + 1/10 + 1/15 = 10/30 or 1/3
They worked together for two days. Therefore, total work done in 2 days by all of them working together = (1/3)*2 = 2/3

Alex & Bill quit after 2 days. Charles has to do the remaining work all by himself. 
Total work done = 2/3
Amount of work remaining = 3 - 2/3 = 1/3

If Charles can do 1/15th of the work in 1 day working alone. So, he will be able to finish the remaining work in (1/3)/(1/15) = 5 days

Kinshook · Answer

Given: Alex takes 6 days to complete a work, while Bill takes 10 days to complete the work alone. Charles takes 15 days to complete the work alone. All of them work together for 2 days. Then Alex and Bill quit. 
Asked: How many days more will it take Charles to do the remaining work alone?

Work done in 2 days = 2/6 + 2/10 + 2/15 = 2(15+9+6)/90 = 2/3
Word remaining = 1/3

Time required by Charles = 15/3 = 5 days

IMO C

GeorgeA11 · Answer

I would suggest percentages..as a tool

This method is faster. We can use percentages to solve.

Alex completes 100% of work in 6 days. Bill completes 100% of work in 10 days. Charles completes 100% of work in 15 days.

In 2 days Alex completes

Lets construct a table

Days Percentage

6 100%

2 ??

Cross multiplying = 2x100/6 =33.33 %

In 2 days Alex completes =33.33% of work

Similarly

Bill completes 100% of work in 10 days.

In 2 days Bill completes 20% of the work

Charles completes 100% of work in 15 days.

In 2 days Bill completes 13.33% of the work

Total work completed = 33.33 +20 +13.33= 66.66%

Remaining work = 100-66.66 = 33.33%

Charles completes 100% of work in 15 days.

In how many days he will complete 33.33%

Percentage Days

100% 15

33.33 ??

Cross multiplying

= 33.33x15 / 100 = 5 days

Take away: You can use percentages as a tool to save time and minimize calculations.

To reach me:
My linkedin profile: https://www.linkedin.com/in/georgeanand/
My facebook learning group: https://www.facebook.com/groups/semanticsGMAT

Do check out my other blog posts here: https://letsgmat.blogspot.com/

ScottTargetTestPrep · Answer

Solution:

The rates of Alex, Bill and Charles are 1/6, 1/10 and 1/15, respectively. After two days of working together 2 x (1/6 + 1/10 + 1/15) = 2 x (5/30 + 3/30 + 2/30) = 2 x 10/30 = 2 x 1/3 = 2/3 of the job is completed. Therefore, the remaining 1/3 of the job will be completed by Charles alone in (1/3) / (1/15) = 1/3 x 15 = 5 days.

Answer: C

Alex takes 6 days to complete a work, while Bill takes 10 days to comp

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