Question

$A$ is $30$% more efficient than $B$. How much time will they, working together, take to complete a job which $A$ alone could have done in $23$ days?

• A. $11$ days
• B. $13$ days
• C. $20\frac{3}{17}$ days
• D. None of these

Answer 1

Answer: (B)

$13$ days

Ratio of times taken by $A$ and $B$ $=100:130=10:13$.
Suppose $B$ takes $x$ days to do the work.
Then, $10:13::23:x$ $\Rightarrow$ $x=\left(\frac{23\times 13}{10}\right)\Rightarrow x=\frac{299}{10}$.
$A$'s $1$ day's work $=\frac{1}{23}$;
$B$'s $1$ day's work $=\frac{10}{299}$;
$(A+B)$'s $1$ day's work $=(\frac{1}{23}+\frac{10}{299})=\frac{23}{299}=\frac{1}{13}$
Therefore, $A$ and $B$ together can complete the work in $13$ days.