Question

Choose the most appropriate option.
'A' and 'B' complete a work in $12$ days, 'B' and 'C' in $8$ days and 'C' and 'A' in $16$ days. 'A' left after working for $3$ days. In how many days more will 'B' and 'C' finish the remaining work?

• A. $7\frac{3}{4}$
• B. $6\frac{5}{6}$
• C. $4\frac{3}{4}$
• D. $3\frac{3}{4}$.

Answer 1

Answer: (C)

$4\frac{3}{4}$

$A$ and $B$ complete a work in $12$ days

$A$ and $B$ complete a work in $1$ day,

$\Rightarrow$ $A+B=\frac{1}{12}$ ----- ( 1 )

$B$ and $C$ complete a work in $8$ days

$B$ and $C$ complete a work in $1$ day,

$\Rightarrow$ $B+C=\frac{1}{8}$ ----- ( 2 )

$C$ and $A$ complete a work in $16$ days

$C$ and $A$ complete a work in $1$ day,

$\Rightarrow$ $A+C=\frac{1}{16}$ ----- ( 3 )

Solving equation ( 2 ) and ( 3 ), we get

$\Rightarrow$ $B-A=\frac{1}{16}$ ----- ( 4 )

Solving equation ( 1 ) and ( 4 ) we get,

$B=\frac{7}{96}$ and $A=\frac{1}{96}$

Assuming $A$ and $B$ and $C$ start the work.

If $A$ and $B+C$ works for $3$ days, work completed in $1$ day is

$\Rightarrow$ $\frac{1}{8}+\frac{1}{96}=\frac{13}{96}$

Work in $3$ days $=\frac{13}{96}\times 3=\frac{13}{32}$

Balance work is done in $1$ day, how many days to complete $\frac{19}{32}th$ work $=\frac{19}{32}\times 8$

$=\frac{19}{4}days$

$=4\frac{3}{4}days$