Tag: ratio and proportion

Quizzes (7) Questions (130)

Questions Related to ratio and proportion

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

If $\dfrac {x}{y}=\dfrac {3}{4}$ and $\dfrac {x}{2z}=\dfrac {3}{2}$, then $\dfrac {2x+z}{x-2z}+\left (\dfrac {6}{7}+\dfrac {y-x}{y+x}\right )$ will be equivalent to

  1. 8

  2. 9

  3. 11

  4. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\because \dfrac {x}{y}=\dfrac {3}{4}\Rightarrow \dfrac {y-x}{y+x}=\dfrac{4-3}{4+3}=\dfrac {1}{7}$
$\because \dfrac {x}{2z}=\dfrac {3}{2}\Rightarrow 2x=6z$ or, $x=3z$
$\therefore \dfrac {2x+z}{x-2z}+\left (\dfrac {6}{7}+\dfrac {y-x}{y+x}\right )=\dfrac {6z+z}{3z-2z}+\left (\dfrac {6}{7}+\dfrac {1}{7}\right )$
$=\dfrac {7z}{z}+\dfrac {7}{7}=7+1=8$.

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

After applying invertendo to $3:7::2:9$ we get

  1. $3:7::2:9$

  2. $3:2::7:9$

  3. $9:7::2:3$

  4. $7:3::9:2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If $a : b :: c : d$ then $b : a :: d : c$ is invertendo property of ratios

We have $3:7::2:9$
After applying invertendo we get
$7:3::9:2$
Option D is correct

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

If $x=7-4\sqrt 3$, the value of $x^2+\displaystyle\frac{1}{x^2}$ will be

  1. $146$

  2. $148$

  3. $194$

  4. $196$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given,
$x=7-4\sqrt 3$
$\therefore \displaystyle\frac{1}{x}=\displaystyle\frac{1}{(7-4\sqrt 3)}\times \displaystyle\frac{7+4\sqrt 3}{7+4\sqrt 3}$
$=\displaystyle\frac{7+4\sqrt 3}{(49-48)}$
$=7+4\sqrt 3$
Now,
$x+\displaystyle\frac{1}{x}=(7-4\sqrt 3)+(7+4\sqrt 3)$
$=14$
$=> \left( x+\displaystyle\frac{1}{x}\right)^2=(14)^2$
Using $(a+b)^2=a^2+b^2+2ab$ we get,
$=> x^{ 2 }+\frac { 1 }{ x^{ 2 } } +2(x)(\frac { 1 }{ x } )=196$
$=> x^2+\displaystyle\frac{1}{x^2}=196-2$
$\therefore x^2+\displaystyle\frac{1}{x^2}=194$

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

If $x=3+\sqrt 8$ then the value of $x^2+\frac {1}{x^2}$ is

  1. 30

  2. 32

  3. 34

  4. 36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$x=3+\sqrt 8\Rightarrow \frac {1}{x}=\frac {1}{3+\sqrt 8}\times \frac {3-\sqrt 8}{3-\sqrt 8}=\frac {3-\sqrt 8}{9-8}$
$=3-\sqrt 8$
$x^2+\frac {1}{x^2}=\left (x+\frac {1}{x}\right )^2-2=36-2=34$

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

If $a : b :: c : d$ then $b : a :: d : c$. This property is known as :

  1. Invertendo property

  2. Alternendo property

  3. Componendo property

  4. Dividendo property
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If $a : b :: c : d$ then $b : a :: d : c\Rightarrow $invertendo property.

proof
$\dfrac{a}{b}=\dfrac{c}{d}$

inverting both sides, we get
$\Rightarrow \dfrac{b}{a}=\dfrac{d}{c}$

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

After applying invertendo to $31:15::18:19$  we get $15:a::b:18$ 
What is the value of $a+b$

  1. $40$

  2. $50$

  3. $30$

  4. $60$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If $a : b :: c : d$ then $b : a :: d : c$ is invertendo property of ratios

We have $31:15::18:19$
After applying invertendo we get
$15:31::19:18\equiv  15:a::b:18\ a+b=31+19=50$
Option B is correct

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

Find the value of $a$ and $b$ respectively
After applying invertendo to $2:5::3:9$  we get $a:2::9:b$ 

  1. $9$ and $2$

  2. $2$ and $9$

  3. $3$ and $5$

  4. $5$ and $3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If $a : b :: c : d$ then $b : a :: d : c$ is invertendo property of ratios

We have $2:5::3:9$
After applying invertendo we get
$5:2::9:3\equiv a:2::9:b$
$\Rightarrow a=5,b=3$
Option D is correct

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

Here 'x' in the following is : $\dfrac{\sqrt{a+x}+\sqrt{a-x}}{\sqrt{a+x}-\sqrt{a-x}}=b$

  1. $\dfrac{2ab}{(b^2+1)}$

  2. $\dfrac{2ab}{a+b}$

  3. $\dfrac{a+b}{2ab}$

  4. $\dfrac{b^2+1}{2ab}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\dfrac{\sqrt{a+x}+\sqrt{a-x}}{\sqrt{a+x}-{\sqrt{a-x}}}=\dfrac{b}{1}$

$\Rightarrow \dfrac{\sqrt{a+x}}{\sqrt{a-x}}=\dfrac{b+1}{b-1}$

$\Rightarrow \dfrac{a+x}{a-x}=\dfrac{(b+1)^2}{(b-1)^2}$

$\Rightarrow \dfrac{(a+x)+(a-x)}{(a+x)-(a-x)}=\dfrac{(b+1)^2+(b-1)^2}{(b+1)^2-(b-1)^2}$

$\Rightarrow \dfrac{2a}{2x}=\dfrac{2(b^2+1)}{4b}$

$\Rightarrow x=\dfrac{2ab}{b^2+1}$