Question

$A$ is 3 times more efficient than $B$. Hence, he takes 60 days less in painting a room. In how many days, work will be completed, if $A$ and $B$ both work together ?

• A. 30 days
• B. 45 days
• C. $22\frac{1}{2}$ days
• D. $17\frac{1}{2}$ days

Answer 1

Answer: (C)

$22\frac{1}{2}$ days

Let $A$ takes ${}^{\prime }{n}^{\prime }$ days to paint the room.
So $B$ will take $3n$ days to paint the room.
$\Rightarrow 3n-n=60$
or $n=30$
$\Rightarrow A=30,B=90$
$A$ & $B$ will do $\frac{1}{30}+\frac{1}{90}=\frac{4}{90}=\frac{2}{45}$ work in a day.
So they will complete the work in $\frac{45}{2}=22\frac{1}{2}$ days.