Question

$A$ and $B$ can do a work in $10$ days, $B$ and $C$ in $15$ days and $A$ and $C$ in $12$ days. In how many days the work will be finished by $A,B$ and $C$ working together.

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is C $8$

According to the question-

$\frac{1}{A}+\frac{1}{B}=\frac{1}{10}.....\left(1\right)$

$\frac{1}{B}+\frac{1}{C}=\frac{1}{15}.....\left(2\right)$

$\frac{1}{C}+\frac{1}{A}=\frac{1}{12}.....\left(3\right)$

Adding equation $\left(1\right),\left(2\right)\&\left(3\right)$, we have

$(\frac{1}{A}+\frac{1}{B})(\frac{1}{B}+\frac{1}{C})+(\frac{1}{C}+\frac{1}{A})=\frac{1}{10}+\frac{1}{15}+\frac{1}{12}$

$\Rightarrow 2(\frac{1}{A}+\frac{1}{B}+\frac{1}{C})=\frac{6+4+5}{60}$

$\Rightarrow \frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{15}{2\times 60}=\frac{1}{8}$

Hence the work will be finished in $8$ days by $A,B$ and $C$ working together.