Question : Rs.11,500 has to be divided between X, Y, and Z such that X gets $\frac{4}{5}$th of what Y gets and Y gets $\frac{2}{3}$rd of what Z gets. How much more does Z get over X (in Rs.)?

Option 1: 7200

Option 2: 1800

Option 3: 1170

Option 4: 2450

Question : Three fractions $x, y$ and $z$ are such that $x > y > z$. When the smallest of them is divided by the greatest, the result is $\frac{9}{16}$, which exceeds $y$ by 0.0625. If $x+y+z=2 \frac{3}{12}$, then what is the value of $x + z$?

Option 1: $\frac{5}{4}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{7}{4}$

Option 4: $\frac{1}{4}$

Question : The value of $\frac{(x-y)^3+(y-z)^3+(z-x)^3}{6(x-y)(y-z)(z-x)}$, where $x \neq y \neq z$, is equal to:

Option 1: $\frac{1}{4}$

Option 2: $\frac{1}{2}$

Option 3: $\frac{1}{3}$

Option 4: $\frac{1}{9}$

Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{(y z)}+\frac{y^2}{(x z)}+\frac{z^2}{(x y)}$?

Option 1: 1

Option 2: 0

Option 3: 2

Option 4: 3

Question : What is the simplified value of $\frac{(x+y+z)(x y+y z+z x)–x y z}{(x+y)(y+z)(z+x)}$?

Option 1: $y$

Option 2: $z$

Option 3: $1$

Option 4: $x$

Question : Simplify $\frac{1}{2 + 2 p} + \frac{1}{2 + 2 q} + \frac{1}{2 + 2 r}$, where $p = \frac{x}{y + z}$, if $q = \frac{y}{z + x}$ and $r = \frac{z}{x + y}$.

Option 1: $1$

Option 2: $x+y+z$

Option 3: $2$

Option 4: $\frac{1}{2}$