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 the painting 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 $n=30$
$\Rightarrow A$ takes $30$ days and $B$ takes $90$ days.
$A$ & $B$ 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.
Hence, option $C$ is the correct answer.