Question

$A$ and $B$ together can do a piece 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 it in $13$ days. In how many days $C$ alone will do the work ?

• A. $16$ days
• B. $24$ days
• C. $36$ days
• D. $48$ days

Answer 1

Answer: (B)

$24$ days

Work done by (A+B)'s in 1 day$=\frac{1}{12}$

work done by (B+C)'s in 1 day$=\frac{1}{16}$

Let C does a work in x days

Then work done by C in a day$=\frac{1}{x}$

According to the questio

A's 5 day's work+B's 7 day's work+C's 13 day's work=1

(A+B)'s 5 day's+(B+C)'s 2 days+C's 11 day's

$\frac{5}{12}+\frac{2}{16}+\frac{11}{x}=1$

$\frac{11}{x}=1-\frac{5}{12}-\frac{2}{16}$

$\frac{11}{x}=\frac{22}{48}$

$x=24days$