Question

$A$ is three times more efficient worker than $B$ and is therefore able to complete a work in $60$ days less than $B$. What is the number of days that $A$ and $B$ together will take to complete the work?

• A. $22.5$ days
• B. $22$ days
• C. $24.5$ days
• D. $24$ days

Answer 1

Answer: (A)

$22.5$ days

Let $A$ complete the work in $x$ days. Then, $B$ will complete the same work in $3x$ days.

Given:-

$3x-x=60$ $\Rightarrow$ $x=30$ days

$\therefore$ $A$ will complete the work in $30$ days.

$\Rightarrow$ $B$ will complete the work in $3\times 30$ $=90$ days.

$(A+B{)}^{\prime }$s $1$ day work $=\frac{1}{30}+\frac{1}{90}=\frac{4}{90}$

$\Rightarrow$ $(A+B)$ will complete the work in $\frac{90}{4}$ days $=22.5$ days