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

(A's 1 day's work) : (B's 1 day's work)
$$\eqalign{ & = \frac{7}{4}:1 \cr & = 7:4 \cr} $$
Let A's and B's 1 day's work be 7x and 4x respectively
Then,
$$\eqalign{ & 7x + 4x = \frac{1}{7} \cr & \Rightarrow 11x = \frac{1}{7} \cr & \Rightarrow x = \frac{1}{{77}} \cr & \therefore {\text{A's 1 day's work}} \cr & = \left( {\frac{1}{{77}} \times 7} \right) \cr & = \frac{1}{{11}} \cr} $$
Hence, A alone can do the job in 11 days.