Question

$A$ and $B$ together can complete a work in $12$ days. $A$ alone can complete it in $20$ days. If $B$ does the work only for half a day daily, then in how many days $A$ and $B$ together will complete the work ?

• A. $10$ days
• B. $11$ days
• C. $15$ days
• D. $20$ days

Answer 1

The correct option is C $15$ days

$A$ can complete the work in $20$ days

Work done by $A$ in one day is $\frac{1}{20}$

$A$ and $B$ can complete the wrok in $12$ days

Work done by $A$ and $B$ in one day is $\frac{1}{12}$

So Work done by $B$ in one day is $\frac{1}{12}-\frac{1}{20}=\frac{1}{30}$

$B$ does the work half a day

So the work done by $B$ in a day is $\frac{1}{60}$

Work done $A$ and $B$ in one day is $\frac{1}{20}+\frac{1}{60}=\frac{1}{15}$

Number of days taken by $A$ and $B$ is $15$ days