Tag: ratio and proportions

Questions Related to ratio and proportions

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

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

  1. $2:3:4$

  2. $4:3:2$

  3. $3:2:4$

  4. None of these

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Correct Option: A
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., $a : b: c = 2k : 3k : 4k$

$a : b; c = 2 : 3 : 4$  

If $a:b=3:4$, then $4a:3b=$

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

  1. $4:3$

  2. $3:4$

  3. $1:1$

  4. None of these

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Correct Option: C
Explanation:

Given $a:b=3:4$

or, $\dfrac{a}{b}=\dfrac{3}{4}$
or, $4a={3b}$.....(1).
Now,
$\dfrac{4a}{3b}$
$=\dfrac{3b}{3b}$ [ Using (1)]
$=\dfrac{1}{1}$.
So $4a:3b=1:1$.

What is the compounded ratio of $x : y, y : z$ and $z : w$

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

  1. $y : w$

  2. $x : w$

  3. $y : z$

  4. $x : z$

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Correct Option: B
Explanation:

By the defination of compound ratio these ratio can be expressed as
$\dfrac {x}{y} \times \dfrac {y}{z}\times \dfrac {z}{w} = \dfrac {x}{w}$
Hence $x : w$

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

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

  1. $35:49:66$

  2. $30:42:77$

  3. $30:42:55$

  4. None of these

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Correct Option: B
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 $42$

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

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

$30 : 42 : 77$

The compounded ratio of (2 : 3), (6 : 11), and (11 : 2) is

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

  1. 1:2

  2. 2:1

  3. 11:24

  4. 36:121

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Correct Option: B
Explanation:

Required compounded ratio $\displaystyle=\frac{2}{3}\times\frac{6}{11}\times\frac{11}{2}=2:1$

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

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

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

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

  3. $1 : 1$

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

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Correct Option: D
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 $(x - y)^{2} : (x + y)^{2}$

If $2a=3b=4c$, then $a:b:c=$

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

  1. $2:3:4$

  2. $3:4:6$

  3. $4:3:2$

  4. $6:4:3$

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Correct Option: D
Explanation:

Given, 

$2a=3b=4c$

Now dividing both sides with LCM of $2,3,4$ i.e. $12$ we get,

$\dfrac{a}{6}=\dfrac{b}{4}=\dfrac{c}{3}$

So $a:b:c=6:4:3$

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

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

  1. $5:4:3$

  2. $20:15:12$

  3. $9:12:15$

  4. $12:15:20$

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Correct Option: B
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, $\displaystyle \frac{60}{3} : \frac{60}{4} : \frac{60}{5}$

$= 20 : 15 : 12$

Find the compounded ratio of $4 : 5, 10 : 6$ and $3 : 5$

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

  1. $4 : 5$

  2. $3 : 5$

  3. $2 : 3$

  4. $9 : 11$

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Correct Option: A
Explanation:

By the defination of compound ratio $4 : 5, 10 : 6$ and $3 : 5$ can be expressed as
$\dfrac {4}{5}\times \dfrac {10}{6} \times \dfrac {3}{5} = \dfrac {4}{5}$
Hence $4 : 5$

What is the compounded ratio of $3 : 5, 7 : 9$ and $15 : 28$

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

  1. $1 ; 4$

  2. $5 : 7$

  3. $9 : 8$

  4. $3 : 7$

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Correct Option: A
Explanation:

By the defination of compound ratio these ratio can be expressed as
$\dfrac {3}{5}\times \dfrac {7}{9}\times \dfrac {15}{28} = \dfrac {1}{4}$
Hence $1 : 4$