If a + b = 10 and a/b - 13 = - b/a - 11 then what is the value of 3ab + 4a2 + 5b2?

Answer: Option B

$$\begin{array}{rl}& \text{Let }\sqrt{\frac{a}{b}}=x\\ & \therefore x-13=\frac{-1}{x}-11\\ & x+\frac{1}{x}=2\\ & \therefore x=1\\ & \sqrt{\frac{a}{b}}=1\text{ and }a+b=10\\ & \therefore a=b=5\\ & 3ab+4a^2+5b^2\\ & =3a^2+4a^2+5a^2\\ & =12a^2\\ & =12\times 25\\ & =300\end{array}$$