A and B together can do a peace of work in 12 days, which B and C toge

Question

A and B together can do a peace of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 Days and B for 7 Days, C finishes in 13 days. In how many days C alone will do the work?

A. 13
B. 17
C. 19
D. 21
E. 24

Show Answer

Official Answer

E

A. 13 
B. 17
C. 19
D. 21
E. 24

manideep12 · Accepted Answer

Let's take total work needs to be done is 48 units (LCM of 12 and 16).

Given
A+B can do a 48 units work in 12 days.
In 1 day A+B can do 4 units of work.

B+C can do 48 units of work in 16 days
In 1 day B+C can do 3 units of work.

From question,

5A+7B+13C = 48.

5(A+B)+2B+2C+11C = 48.

5(A+B)+2(B+C)+11 = 48.

5x4+2x3+11C=48.

C = 2 units for 1 day.

So,48 units of work C will take 24 days.

Ans:-E

Stonely · Answer

Practical approach 
A+B do the work alone in 12 days
A+B in 5 days is less than 1/2 done
C takes 13 days to do a little more than 1/2
~26 days for half is close enough to 24 and way to far from 21. 24 E is the answer very quickly

Posted from my mobile device

mehro023 · Answer

Hi,

I am not clear how to solve. can i get a better solution please ?

K

Yellowp · Answer

A and B together can do a peace of work in 12 days, which B and C together can do in 16 days. After A has been working at it for 5 Days and B for 7 Days, C finishes in 13 days. In how many days C alone will do the work?

A. 13
B. 17
C. 19
D. 21
E. 24

Show Answer

Official Answer

E

A. 13
B. 17
C. 19
D. 21
E. 24

A and B together can do a piece of work in 12 days => A+B =1/12 (1)
B and C together can do in 16 days => B+C=1/16 (2)
After A has been working at it for 5 Days and B for 7 Days, C finishes in 13 days => 5A+7B+13C = 1 (3)
In how many days C alone will do the work? => C=?

3 variables & 3 equations so solve C using the equations:
A+B =1/12 (1) => A=1/12 - B (4)
B+C=1/16 (2) => C=1/16-B (5)

Sub (4) & (5) into (3):
5(1/12 - B) +7B + 13(1/16-B) =1
B=1/48

Sub B=1/48 into (5):
C=1/16 - 1/48
C=1/24

BrushMyQuant · Answer

Let's assume following variables/values 
 
 Rate of A = A 
 Rate of B = B 
 Rate of C = C 
 Work Done = 1 (As Work done by everyone is same)  
Formula to be used  Rate * Time = Work

A and B together can do a piece of work in 12 days

=> Combined rate of A and B = A + B
=> Rate * Time = Work
=> (A + B) * 12 = 1
=> A + B = 1/12 ...(1)

B and C together can do in 16 days

=> Combined rate of B and C = B + C
=> Rate * Time = Work
=> (B + C) * 16 = 1
=> B + C = 1/16 ...(2)

After A has been working at it for 5 days and B for 7 days, C finishes in 13 days

Work done by A in 5 days = A * 5 = 5A
Work done by B in 7 days = B * 7 = 7B
Work done by C in 13 days = C * 13 = 13 C

Total Work done = 5A + 7B + 13C = Total Work = 1 
=> 5A + 5B + 2B + 2C + 11C = 1
=> 5*(A + B) + 2*(B + C) + 11C = 1
=> 5*(1/12) + 2*(1/16) + 11C = 1
=> 5/12 + 1/8 + 11C = 1
=> 11C = 1 - 5/12 - 1/8
=> 11C = 24/24 - 10/24 - 3/24 = 11/24
=> C = 1/24

In how many days C alone will do the work?

=> Rate * Time = Work
=> 1/24 * Time = 1
=> Time = 24 days

So,  Answer will be E 
Hope it helps!

Watch following video to MASTER Work Rate Problems

https://www.youtube.com/watch?v=dRxzi_x3ZwY

patpathaha · Answer

A + B = 12 days to finish 1 work => In 1 day, A + B finish 1/12 work
B + C = 16 days to finish 1 work => In 1 day, B + C finish 1/16 work

A work for 5 hours
B work for 7 hours, or 5 hours + 2 hours
C work for 13 hours, or 2 + 11 hours

In 5 hours, A + B did 5 * 1/12 = 5/12 part of the work => 7/12 work left
In the next 2 hours, B+C did 2 * 1/16 = 2/16 = 1/8 part of the work => number of work left for C to work is 7/12 - 1/8 = 11/24 work

For the rest of 11 hours, C have to do 11/24 part of the work alone, so he would need 24 days

A and B together can do a peace of work in 12 days, which B and C toge

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A and B together can do a peace of work in 12 days, which B and C toge

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards