B and C together can complete a work in 8 days, A and B together can complete the same work in 12 days and A and C together can complete the same work in 16 days. In how many days can A, B and C together complete the same work ?

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BANK PO Exam (Andhra Bank) 2009 click here to view all questions

B and C together can complete a work in 8 days, A and B together can complete the same work in 12 days and A and C together can complete the same work in 16 days. In how many days can A, B and C together complete the same work ?

A$$3\frac{9}{13}$$

B$$7\frac{5}{13}$$

C$$7\frac{5}{12}$$

D$$3\frac{5}{12}$$

Akilesh Kharvi ? May 29 '2017 at 14:20

Answer is : \(7\frac{5}{13} \)

Explanation:

(B+C)’s 1 day’s work = \(\frac{1}{8}\)...(i)

(A+B)’s 1 day’s work = \(\frac{1}{12}  \)...(ii)

(A+C)’s 1 day’s work = \(\frac{1}{16} \)...(iii)

On adding all these three equations,

2 (A + B + C)’s 1 day’s work

\(=> \frac{1}{8}+\frac{1}{12}+\frac{1}{16} = \frac{6+4+3}{48}=\frac{13}{48}\)

=>(A + B + C)’s 1 day’s work = \(\frac{13}{96}\)

\(\therefore\) A, B and C together can complete the work in \( \frac{96}{13}= 7\frac{5}{13}\) days

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Answer is : \(7\frac{5}{13} \) Explanation: (B+C)’s 1 day’s work = \(\frac{1}{8}\)...(i) (A+B)’s 1 day’s work = \(\frac{1}{12}  \)...(ii) (A+C)’s 1 day’s work = \(\frac{1}{16} \)...(iii) On adding all these three equations, 2 (A + B + C)’s 1 day’s work \(=> \frac{1}{8}+\frac{1}{12}+\frac{1}{16} = \frac{6+4+3}{48}=\frac{13}{48}\) =>(A + B + C)’s 1 day’s work = \(\frac{13}{96}\) \(\therefore\) A, B and C together can complete the work in \( \frac{96}{13}= 7\frac{5}{13}\) days Akilesh Kharvi ? answered May 29 '2017 at 14:20 All Comments

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