Question : If $60 \% \text{ of} (x-y)= 45\%(x+y)$ and $y= k \% \text{ of} \ x$, then $21\%$ of $k$ is equal to:
Option 1: 7
Option 2: 1
Option 3: 6
Option 4: 3
Correct Answer: 3
Solution : Given: $60 \% \text{ of} (x-y)= 45\%(x+y)$ and $y= k \% \text{ of} \ x$ So, $\frac{60}{100} \times (x-y)= \frac{45}{100}(x+y)$ ⇒ $60x-60y=45x+45y$ ⇒ $15x=105y$ ⇒ $\frac{x}{y}=\frac{7}{1}$ ⇒ $x:y=7:1$ Given, $y= \frac{k}{100}\times x$ Putting the values, we get: $1= \frac{k}{100}\times 7$ ⇒ $k= \frac{100}{7}$ $\therefore 21\%$ of $k$ = $\frac{21}{100}\times\frac{100}{7}$ = 3 Hence, the correct answer is 3.
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Question : If $x^4+x^2 y^2+y^4=133$ and $x^2-x y+y^2=7$, then what is the value of $xy$?
Option 1: 8
Option 2: 12
Option 3: 4
Option 4: 6
Question : If $x^4+y^4=x^2 y^2$, then the value of $x^6+y^6$ is:
Option 1: 2
Option 2: 0
Option 3: 1
Question : If $\frac{x}{4 y}=\frac{3}{4}$ then, the value of $\frac{2 x+3 y}{x–2 y}$ is:
Option 2: 9
Option 4: 8
Question : If $x+y+z=13,x^2+y^2+z^2=133$ and $x^3+y^3+z^3=847$, then the value of $\sqrt[3]{x y z}$ is:
Option 1: $8$
Option 2: $7$
Option 3: $-9$
Option 4: $-6$
Question : If $\frac{x^{3}+3y^{2}x}{y^{3}+3x^{2}y}=\frac{35}{19}$, what is $\frac{x}{y} =?$
Option 1: $\frac{7}{6}$
Option 2: $\frac{5}{6}$
Option 3: $\frac{5}{1}$
Option 4: $\frac{7}{1}$
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