If $x = (0.25)^{\frac{1}{2}}, y = (0.5)^{2}, z = (0.216)^{\frac{1}{3}},$ then

$A$ boy was asked to multiply a given number by $\frac{8}{17}$. Instead,he divided it by $\frac{8}{17}$ and got the result $225$ more than what he should have got if he had multiplied the number by $\frac{8}{17}$. The given number was:

Two-fifth of one-fourth of three-seventh of a number is $15$. What is half of that number?

$A$ person was to multiply a fraction by $\frac{6}{7}$. Instead,he divided the fraction by $\frac{6}{7}$ and got an answer which exceeds the correct answer by $\frac{1}{7}$. The correct answer is:

The difference between two numbers is $9$ and the difference between their squares is $207$. The numbers are

If $\left(\frac{x}{y}\right)^{5a-3} = \left(\frac{y}{x}\right)^{17-3a}$,what is the value of $a$?