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The answer is A.

If I select option A --> A = 24 days, B = 36 days, C = 18 days.
Work rate is: A=1/24, B=1/36, C=1/18 task/day

Now taking this statement: After A worked for 8 days, B for 12 days C takes up and finishes it alone in 6 days.

A worked for 8 days --> A finished 8/24=1/3 of the total work
B worked for 12 days --> B finished 12/36=1/3 of the total work
C worked for 6 days --> C finished 6/18=1/3 of the total work

Other options won't fit. Correct me if I am wrong.
This seems a very decent approach!

I formed the equation

72a/5 + 72b/5 = 12b + 12c = 8a + 12b + 6c

Now we have to extract 3 equations from the above and solve for 3 variables. That gets very complicated.
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A and B together can do a piece of work in 72/5 days; B and C together can do a piece of work in 12 days. After A worked for 8 days, B for 12 days C takes up and finishes it alone in 6 days. In how many days will each of them do the work, working alone?

A. A = 24 days, B = 36 days, C = 18 days.
B. A = 24 days, B = 36 days, C = 16 days.
C. A = 24 days, B = 36 days, C = 12 days.
D. A = 24 days, B = 32 days, C = 18 days.
E. A = 24 days, B = 30 days, C = 18 days.


Set A, B, C as the rates and treat an entire piece as 1 job. Then we have the following equations:

(1) \(A + B = \frac{5}{72}\)

(2) \(B + C = \frac{1}{12}\)

(3) \(8A + 12B + 6C = 1\)

First do (3) - 8*(1) to get: \(4B + 6C = 1 - \frac{5}{9} = \frac{4}{9}\)

Subtract 4*(2) from the above to get: \(2C = \frac{4}{9} - \frac{1}{3} = \frac{1}{9}\)

Thus \(C = \frac{1}{18}\) which means C takes 18 days alone. Then we can plug this in (2) to get \(B = \frac{1}{12} - \frac{1}{18} = \frac{1}{36}\).

Now we can confirm the answer must be A.

Ans: A
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For this question, we can benefit from first looking at the answer choice. All the option has A = 24 days. So, we have the answer for A already.

Now we know that (1/A) + (1/B) = (5/72) --> Put A = 24 and solve for B --> B = 36 days
Simillarly, (1/B) + (1/C) = (1/12) --> Put B = 36 and solve for C --> C = 18 days.

Answer is A
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I totally agree with the explanations given above. Just thought of giving another approach by using the answer choices.

If you analyze the answer choices, Did you notice something interesting?

A = 24 days is common in all answer choices.

My next question is can we use it to solve the question? Yes. you can.
we can confirm that A will take 24 days to finish the work alone. Using this data will help you to save some time.

LCM approach is more convenient here. Lets assume the total work = LCM ( 72,12,24) = 72 units.

Since we are asked to calculate the time taken by A, B, and C to finish the work alone, we need to calculate the individual rate of A, B and C respectively.
By using the data from answer choices, we can easily find the rate of A.

Rate of A = 72/24 = 3 units / day . As A can complete the work in 24 days working alone.


Rate of A and B = 72/(72/5) = 5 units/day

Rate of B = 5 - 3 = 2 units/day

Rate of B and C = 72/12 = 6 units /day.

Rate of C = 6 - 2 = 4 units /day

Since we know the individual rates of B and C, it's very easy to calculate the time taken by each of them to complete the work alone.

Time taken by B alone = Total work / Rate of B = 72/2 = 36 days

Time taken by C alone = Total work / Rate of C = 72/4 = 18 days.

Option A is the answer.

Remember, you can always use the answer choices to your advantage.

Thanks,
Clifin J Francis,
GMAT QUANT SME
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Bunuel
A and B together can do a piece of work in 72/5 days; B and C together can do a piece of work in 12 days. After A worked for 8 days, B for 12 days C takes up and finishes it alone in 6 days. In how many days will each of them do the work, working alone?

A. A = 24 days, B = 36 days, C = 18 days.
B. A = 24 days, B = 36 days, C = 16 days.
C. A = 24 days, B = 36 days, C = 12 days.
D. A = 24 days, B = 32 days, C = 18 days.
E. A = 24 days, B = 30 days, C = 18 days.

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

Say there are 72 units of work.

A and B together do 72/(72/5) = 5 units every day.
B and C together do 72/12 = 6 units every day.

(A worked for 8 days + B worked for 8 days) + (B worked for 4 days + C worked for 4 days) + C worked for 2 days = 72

5 * 8 + 4 * 6 + C worked for 2 days = 72

So C does 4 units of work every day. Then B does 2 units every day and A does 3 units every day.

Time taken by A = 72/3 = 24 days, by B = 72/2 = 36 days, by C = 72/4 = 18 days

Answer (A)

@Experts
How to come up with this equation/ How it is derived?

(A worked for 8 days + B worked for 8 days) + (B worked for 4 days + C worked for 4 days) + C worked for 2 days = 72

I understood the total work is 72 units but where it is mentioned that A and B together worked for 8 days, B worked for 12 days and in total and I am confused in the question stem when C was introduced?
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this took me a looooong while. but i eventually went wit hmy instincts.. my take away here.

so we have

(A+B) = (5/72) ..............................................f(1)
(C+B)=(1/12)................................................f(2)
A works for 8 days with B i.e. 8*(A+B)
B works alone for a further 4 hours i.e. 4(B)
C works alone for 6 hours 6(C)

Which gives us 8(A+B)+4(B)+6(C)=.................f(3)
Sub f(1) into f(3)

8(5/72)+4(B)+6(C)=1
simplify to 4(B)+6(C)=(4/9)............................f(4)

from f(2) B=(1/12)-C.....................................f(5)
sub f(4) in into f(5)

4[(1/12)-C]+6C=(4/9), which simplifies to C=1/18, i.e. rate for C meaning C alone takes 18 days

sub C=1/18 in to f(2) for B=1/36, i rate for B alone meaning B takes 36 days

sub B=1/36 into f(1) for a=1/24. i.e. rate for A , meaning A takes 24 days

Answer A.

..............................fin.............
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Hi Karishma,
Did'nt the question say A's individual work for 8 days followed by B's 12 days and the remaining work by C alone?
KarishmaB
Bunuel
A and B together can do a piece of work in 72/5 days; B and C together can do a piece of work in 12 days. After A worked for 8 days, B for 12 days C takes up and finishes it alone in 6 days. In how many days will each of them do the work, working alone?

A. A = 24 days, B = 36 days, C = 18 days.
B. A = 24 days, B = 36 days, C = 16 days.
C. A = 24 days, B = 36 days, C = 12 days.
D. A = 24 days, B = 32 days, C = 18 days.
E. A = 24 days, B = 30 days, C = 18 days.

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

Say there are 72 units of work.

A and B together do 72/(72/5) = 5 units every day.
B and C together do 72/12 = 6 units every day.

(A worked for 8 days + B worked for 8 days) + (B worked for 4 days + C worked for 4 days) + C worked for 2 days = 72

5 * 8 + 4 * 6 + C worked for 2 days = 72

So C does 4 units of work every day. Then B does 2 units every day and A does 3 units every day.

Time taken by A = 72/3 = 24 days, by B = 72/2 = 36 days, by C = 72/4 = 18 days

Answer (A)
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this is the most easiest and fastest way. Great observation and application of mind
Dvaishnav
For this question, we can benefit from first looking at the answer choice. All the option has A = 24 days. So, we have the answer for A already.

Now we know that (1/A) + (1/B) = (5/72) --> Put A = 24 and solve for B --> B = 36 days
Simillarly, (1/B) + (1/C) = (1/12) --> Put B = 36 and solve for C --> C = 18 days.

Answer is A
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