Tag: ratio and proportion

Quizzes (7) Questions (130)

Questions Related to ratio and proportion

Multiple choice composition of ratios types of ratios ratio and proportions ratio and proportion maths

If $\cfrac{a}{2}=\cfrac{b}{3}=\cfrac{c}{4}$, then $a:b:c=$

  1. $2:3:4$

  2. $4:3:2$

  3. $3:2:4$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, $\displaystyle \frac{a}{2} = \frac{b}{3} = \frac{c}{4}$


Lets take $\displaystyle \frac{a}{2} = \frac{b}{3} = \frac{c}{4} = k$


So, $\dfrac{a}{2}  = k$

$a = 2k$

$\dfrac{b}{3}  = k$

$b = 3k$

$\dfrac{c}{4} = k$

$c = 4k$

i.e., $a : b: c = 2k : 3k : 4k$

$a : b; c = 2 : 3 : 4$  

Multiple choice composition of ratios types of ratios ratio and proportions ratio and proportion maths

If $a:b=5:7$ and $b:c=6:11$, then $a:b:c=$

  1. $35:49:66$

  2. $30:42:77$

  3. $30:42:55$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\dfrac{a}{b} = \dfrac{5}{7} $       $\dfrac{b}{c} = \dfrac{6}{11}$


$\left.\begin{matrix} a = \dfrac{5}{7} b \end{matrix}\right|\begin{matrix} c = \dfrac{11 b}{6} \end{matrix}$

$a : b : c$

$\dfrac{5}{7} b : b : \dfrac{11b}{6}$

$\dfrac{5}{7} : 1 : \dfrac{11}{6}$

L.C.M of $7, 6$ is $42$

$\dfrac{5}{7} \times 42 : 42 \times 1 : \dfrac{11}{6} \times 42$

$5 \times 6 : 42 : 11 \times 7$

$30 : 42 : 77$

Multiple choice composition of ratios types of ratios ratio and proportions ratio and proportion maths

Find the compounded ratio of $(x^{2} - y^{2}) : (x^{2} + y^{2})$ and $(x^{4} - y^{4}) : (x + y)^{4}$

  1. $(x - y)^{3} : (x + y)^{3}$

  2. $(x + y)^{2} : (x^{2} - y^{2})$

  3. $1 : 1$

  4. $(x - y)^{2} : (x + y)^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

By the definition of compounded ratio these ratio can be expressed as
$\dfrac {(x^{2} - y^{2})}{(x^{2} + y^{2})} \times \dfrac {(x^{4} - y^{4})}{(x + y)^{4}}$
$\dfrac {(x^{2} - y^{2})}{(x^{2} + y^{2})} \times \dfrac {(x^{2} - y^{2})(x^{2} + y^{2})}{(x + y)^{4}}$
$= \dfrac {(x^{2} - y^{2})^{2}}{(x + y)^{4}}$
$= \dfrac {[(x - y) (x + y)]^{2}}{(x + y)^{4}}$
$= \dfrac {(x - y)^{2}}{(x + y)^{2}}$
Hence $(x - y)^{2} : (x + y)^{2}$

Multiple choice composition of ratios types of ratios ratio and proportions ratio and proportion maths

If $\cfrac{1}{a}:\cfrac{1}{b}:\cfrac{1}{c}=3:4:5$ then $a:b:c$

  1. $5:4:3$

  2. $20:15:12$

  3. $9:12:15$

  4. $12:15:20$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $\displaystyle \frac{1}{a} : \frac{1}{b} : \frac{1}{c} = 3 : 4 : 5$


As, $\dfrac{1}{a} = 3$      So, $\dfrac{1}{3} = a$,


$\dfrac{1}{b} = 4$            So,  $\dfrac{1}{4} = b$,


$\dfrac{1}{c} = 5$             So, $\dfrac{1}{5} = c$


i.e., a : b : c = $\displaystyle \frac{1}{3} : \frac{1}{4} : \frac{1}{5}$

LCM of $3, 4$ and $5$ is $60$

So, multiply with $60$

We get, $\displaystyle \frac{60}{3} : \frac{60}{4} : \frac{60}{5}$

$= 20 : 15 : 12$