Question

$A$ and $B$ together can finish a work in $30$ days. They worked on it for $20$ days and then $B$ left the work. The remaining work was done by $A$ alone in $20$ days more. In how many days can $A$ alone finish the work?

• A. $48days$
• B. $50days$
• C. $54days$
• D. $60days$

Answer 1

The correct option is D $60days$

Let the total work be $60$ units. [LCM of $30$ and $20$]
$A$ and $B$ do $\frac{60}{30}=2units/day$
As they worked for $20$ days, they did $20\times 2=40units$ of work.
Work left is $60-40=20units$
Thus, $20$ units is finished by $A$ in $20days$.
Hence, $A$ does $\frac{20}{20}=1unit/day$.
So, $A$ alone can finish the work in $\frac{60}{1}=60days$.