Properties of inequalities

$$b/a = (1+1/60)^{60} * 1/60$$
$$\lim x\rightarrow \infty (1+\frac{1}{n})^{n} = e$$
e is also called as Euler's number.
e ~ 2.718
=>$$(1+1/60)^{60} * 1/60< e/60$$
Hence, a/b > 60/e >10

Let $$f\left(x\right)=\ \dfrac{\ y+x}{y+2x}$$

We need to find the minimum and maximum values of f(x)

$$f\left(x\right)=\ \dfrac{\ y+x}{y+2x}=\dfrac{1}{\ \dfrac{\ y+2x}{y+x}}=\dfrac{1}{1+\dfrac{x}{y+x}}=\dfrac{1}{1+\dfrac{1}{\ \dfrac{\ y+x}{x}}}=\dfrac{1}{1+\dfrac{1}{1+\dfrac{y}{x}}}$$

$$f(x)$$ is minimum when $$\dfrac{y}{x}$$ is minimum, i.e. y is minimum and x is maximum

Therefore, y = 4 and x= 3

$$f\left(x\right)=\dfrac{1}{1+\dfrac{1}{1+\dfrac{4}{3}}}=\dfrac{7}{10}$$

$$f(x)$$ is maximum when $$\dfrac{y}{x}$$ is maximum, i.e. y is maximum and x is minimum

Therefore, y = 5 and x = 2

$$f\left(x\right)=\dfrac{1}{1+\dfrac{1}{1+\dfrac{5}{2}}}=\dfrac{7}{9}$$

The answer is option C.