Question

$A$ and $B$ can do a job together in $7$ days. $A$ is $1\frac{3}{4}$ times as efficient as $B$. The same job can be done by $A$ alone in:

• A. $9\frac{1}{3}$ days
• B. $11$ days
• C. $12\frac{1}{4}$ days
• D. $16\frac{1}{3}$ days

Answer 1

The correct option is B $11$ days

($A$'s $1$ day's work):($B$'s $1$ day's work)$=\frac{7}{4}=7:4$.
Let $A$'s and $B$'s $1$ day's work be $7x$ and $4x$ respectively.
Then, $7x+4x=\frac{1}{7}$ $\Rightarrow$ $11x=\frac{1}{7}$ $\Rightarrow$ $x=\frac{1}{77}$
$\therefore$ $A$'s $1$ day's work $=(\frac{1}{77}\times 7)=\frac{1}{11}$.