Tag: properties of proportion

Questions Related to properties of proportion

If $x=\cfrac { 2\sqrt { 5 }  }{ \sqrt { 3 } +\sqrt { 5 }  } $, then what is the value of $\cfrac { x+\sqrt { 5 }  }{ x-\sqrt { 5 }  } +\cfrac { x+\sqrt { 3 }  }{ x-\sqrt { 3 }  } $

properties of proportion ratio and proportions ratio and proportion maths

  1. $\sqrt {5}$

  2. $\sqrt {3}$

  3. $\sqrt {15}$

  4. $2$

Show answer
Correct Option: D
Explanation:

$x=\cfrac { 2\sqrt { 5 }  }{ \sqrt { 3 } +\sqrt { 5 }  } \Rightarrow \cfrac { x }{ \sqrt { 3 }  } =\cfrac { 2\sqrt { 5 }  }{ \sqrt { 3 } +\sqrt { 5 }  } $
and $\cfrac { x }{ \sqrt { 5 }  } =\cfrac { 2\sqrt { 3 }  }{ \sqrt { 3 } +\sqrt { 5 }  } $
Applying components and dividendo, we get
$\cfrac { x+\sqrt { 5 }  }{ x-\sqrt { 5 }  } =-\left( 7+2\sqrt { 15 }  \right) $
and
$\cfrac { x+\sqrt { 3 }  }{ x-\sqrt { 3 }  } =9+2\sqrt { 15 } $
$\Rightarrow \cfrac { x+\sqrt { 5 }  }{ x-\sqrt { 5 }  } +\cfrac { x+\sqrt { 3 }  }{ x-\sqrt { 3 }  } =2$

Which of the following ratios is equal to $13:4$ in its simplest form?

properties of proportion ratio and proportions ratio and proportion maths

  1. $18:8$

  2. $105:36$

  3. $91:28$

  4. $144:250$

Show answer
Correct Option: C
Explanation:

A.  $18 : 8 = \dfrac{18}{8}$

      Cancelling both numerator and denominator by $2$, the ratio becomes $9 : 4$
      Hence this option is wrong.

B. $105 : 36 = \dfrac{105}{36}$
    Cancelling both numerator and denominator by $3$, the ratio becomes $35 : 12$
     Hence this option is wrong.

C.  $91 : 28 = \dfrac{91}{28}$
      Cancelling both numerator and denominator by $7$, the ratio becomes $13 : 4$
      Therefore this is correct option. 

D.  $144 : 250 = \dfrac{144}{250}$
      Cancelling both numerator and denominator by $2$, the ratio becomes $72 : 125$
      Hence this option is also wrong. 

If $a : b = 3 : 5$  then $ a - b : a + b =$

properties of proportion ratio and proportions ratio and proportion maths

  1. $\displaystyle \frac{-1}{4}$

  2. $\displaystyle \frac{1}{4}$

  3. $-4$

  4. $4$

Show answer
Correct Option: A
Explanation:

Let $a = 3x$ and $b = 5x$.
$\therefore \displaystyle \frac{a-b}{a+b}=\frac{3x-5x}{3x+5x}=\frac{-2x}{8x}=-\frac{1}{4}$

If $\left( {{p^2} + {q^2}} \right)/\left( {{r^2} + {s^2}} \right) = \left( {pq} \right)/\left( {rs} \right)$, then what is the value of $\left( {p - q} \right)/\left( {p + q} \right)$ in terms of $r$ and $s$?

properties of proportion ratio and proportions ratio and proportion maths

  1. $\left( {r + s} \right)/\left( {r - s} \right)$

  2. $\left( {r - s} \right)/\left( {r + s} \right)$

  3. $\left( {r + s} \right)/\left( {r s} \right)$

  4. $\left( {r s} \right)/\left( {r - s} \right)$

Show answer
Correct Option: A

If $ \displaystyle \frac {1}{x} : \frac {1}{y} : \frac {1}{z} = 2:3:5, $ then $x:y:z =?$

properties of proportion ratio and proportions ratio and proportion maths

  1. $2:3:5$

  2. $15:10:6$

  3. $5:3:2$

  4. $6:10:15$

Show answer
Correct Option: B
Explanation:

$\dfrac { 1 }{ x } :\dfrac { 1 }{ y } :\dfrac { 1 }{ z } =\quad 2:3:5\ \dfrac { yz:xz:xy }{ xyz } =\quad 2:3:5\ yz:xz:xy\quad =\quad 2xyz:3xyz:5xyz\ 1:1:1=\quad 2x:3y:5z\ x:y:z=\quad \dfrac { 1 }{ 2 } :\dfrac { 1 }{ 3 } :\dfrac { 1 }{ 5 } =\dfrac { 15:10:6 }{ 30 } \ So,\quad x:y:z\quad is\quad 15:10:6$