Question

$A$ and $B$ together can do a piece of work in $12$ days; $B$ and $C$ can do it in $20$ days while $C$ and $A$ can do it in $15$ days. $A,B$ and $C$ all working together can do it in

• A. $6$ days
• B. $9$ days
• C. $10$ days
• D. ${10}^{1/2}$ days

Answer 1

The correct option is C $10$ days

We know that,

Number of days required by $A$ and $B$ to complete the work $=12$ days

Number of days required by $B$ and $C$ to complete the work $=20$ days

Number of days required by $C$ and $A$ to complete the work $=15$ days

$\therefore$ We can calculate, work done by $A$ and $B$ in $1$ day $=1/12$

Work done by $B$ and $C$ in $1$ day $=1/20$

Work done by $C$ and $A$ in $1$ day $=1/15$

Now, work done by $(A$ and $B)$, $(B$ and $C)$, $(C$ and $A)$ together in $1$ day is given by

The sum is $(A+B)+(B+C)+(C+A)=2(A+B+C)=1/12+1/20+1/15=12/60=1/5$

Hence.

Work done by $A,B,C=1/2\times 1/5=1/10$

$\therefore A,B,C$ can do the work in $10$ days.