Question

$A$ is thrice as good as workman as $B$ and therefore is able to finish a job in $60$ days less than $B$. Working together, they can do it in:

• A. $20$ days
• B. $22\frac{1}{2}$ days
• C. $25$ days
• D. $30$ days

Answer 1

The correct option is B $22\frac{1}{2}$ days

Ratio of times taken by $A$ and $B$ $=1:3$
The time difference is $(3-1)2$ days while $B$ takes $3$ days and $A$ takes $1$ day.
If difference of time is $2$ days, $B$ takes $3$ days.
If difference of time is $60$ days, $B$ takes $(\frac{3}{2}\times 60)=90$ days.
So, $A$ takes $30$ days to do the work.
$A$'s $1$ day's work $=\frac{1}{30}$
$B$'s $1$ day's work $=\frac{1}{90}$
$(A+B)$'s $1$ day's work $=(\frac{1}{30}+\frac{1}{90})=\frac{4}{90}=\frac{2}{45}$
$\therefore$ $A$ and $B$ can do the work in $\frac{45}{2}=22\frac{1}{2}$ days.