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A and B together can do a piece of work in 24 days, which B and C together can do it in 32 days. After A has been working at it for 10 days and B for 14 days, C finishes it in 26 days. In how many days C alone will do the work?
  • a)
    32
  • b)
    36
  • c)
    44
  • d)
    48
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A and B together can do a piece of work in 24 days, which B and C toge...
Correct Answer :- d
Explanation : Work done by (A+B)'s in 1 day = 24
work done by (B+C)'s in 1 day = 32
Let C does a work in x days
Then work done by C in a day = 1/x
According to the question
A's 10 day's work + B's 14 day's work + C's 26 day's work = 1
10A + 14B + 26C = 1 ;
10A + 10B + 4B + 4C + 22C = 1 ;
10(A + B ) + 4( B + C ) + 22C = 1 ;
10( 1/24 ) + 4( 1/32 ) + 22C = 1 ;
10/24 + 4/32 + 22C = 1 ;
13/24 + 22C = 1 ;
22C = 1 - 13/24 ;
22C = 11/24 ;
2C = 1/24 ;
C = 1/48 ;
Therefore , C alone takes 48 days to finish the job.
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Most Upvoted Answer
A and B together can do a piece of work in 24 days, which B and C toge...
A + B = 24 ; A + B = 1/24 ( one day work ) ;

B + C = 32 ; B + C = 1/32 ( one day work ) ;

A,B & C working for 10,14 & 26 days and finishes the work .
I.e. 10A + 14B + 26C = 1 ;

10A + 10B + 4B + 4C + 22C = 1 ;

10(A + B ) + 4( B + C ) + 22C = 1 ;

10( 1/24 ) + 4( 1/32 ) + 22C = 1 ;

10/24 + 4/32 + 22C = 1 ;

13/24 + 22C = 1 ;

22C = 1 - 13/24 ;

22C = 11/24 ;

2C = 1/24 ;

C = 1/48 ;

Therefore , C alone takes 48 days to finish the job.
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Community Answer
A and B together can do a piece of work in 24 days, which B and C toge...
Correct Answer :- d
Explanation : Work done by (A+B)'s in 1 day = 24
work done by (B+C)'s in 1 day = 32
Let C does a work in x days
Then work done by C in a day = 1/x
According to the question
A's 10 day's work + B's 14 day's work + C's 26 day's work = 1
10A + 14B + 26C = 1 ;
10A + 10B + 4B + 4C + 22C = 1 ;
10(A + B ) + 4( B + C ) + 22C = 1 ;
10( 1/24 ) + 4( 1/32 ) + 22C = 1 ;
10/24 + 4/32 + 22C = 1 ;
13/24 + 22C = 1 ;
22C = 1 - 13/24 ;
22C = 11/24 ;
2C = 1/24 ;
C = 1/48 ;
Therefore , C alone takes 48 days to finish the job.
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