A and B can do a job together in 7 days. A is 13/4 times as efficient as B. The same job can be done by A alone in :

Answer: Option B

$$\begin{array}{rl}& \left(\text{A’s}\text{1}\text{day’s}\text{work}\right)\text{:}\left(\text{B’s}\text{1}\text{day’s}\text{work}\right)\\ & =\frac{7}{4}:1=7:4\\ & \text{Let}\text{A’s}\text{and}\text{B’s}\text{1}\text{day’s}\text{work}\text{be}\\ & 7x\text{and}4x\text{respectively}\\ & \text{Then},7x+4x=\frac{1}{7}\\ & \Rightarrow 11x=\frac{1}{7}\\ & \Rightarrow x=\frac{1}{77}\\ & \therefore \text{A’s}\text{1}\text{day’s}\text{work}\\ & =\frac{1}{77}\times \text{7}=\frac{1}{11}\end{array}$$
So, A will do the work in 11 days