Tag: composition of ratios

Questions Related to composition of ratios

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

Show answer
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. $6:4:3$

Show answer
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. $12:15:20$

Show answer
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. $9 : 11$

Show answer
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. $3 : 7$

Show answer
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 $1 : 4$

Find the compounded ratio of $5 : 7, 12 : 8$ and $13 : 6$

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

  1. $65 : 28$

  2. $39 : 12$

  3. $5 : 8$

  4. $6 : 7$

Show answer
Correct Option: A
Explanation:

By the defination of compound ratio $5 : 7, 12 : 8$ and $13 : 6$ can be expressed as
$\dfrac {5}{7}\times \dfrac {12}{8}\times \dfrac {13}{6} = \dfrac {65}{28}$
Hence $65 : 28$

What is the compounded ratio of $9 : 27$ and $4 : 12$

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

  1. $3 : 11$

  2. $2 : 11$

  3. $1 : 9$

  4. $2 : 9$

Show answer
Correct Option: C
Explanation:

By the defination of compound ratio $9 : 27$ and $4 : 12$ can be expressed as
$\dfrac {9}{27} \times \dfrac {4}{12} = \dfrac {1}{9}$
Hence $1 : 9$

Find the compounded ratio of $\dfrac{3}{5}, \dfrac{7}{8}$ and $\dfrac{5}{10}$

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

  1. $\dfrac{21}{80}$

  2. $\dfrac{21}{10}$

  3. $\dfrac{80}{27}$

  4. $\dfrac{5}{11}$

Show answer
Correct Option: A
Explanation:

let be $ a=\dfrac{3}{5}, b=\dfrac{7}{8}, c=\dfrac{5}{10}$
therefore the $ratio=a\times b\times c=\dfrac{3\times 7\times 5}{5\times 8\times 10}=\dfrac{21}{80}$

Find the compounded ratio of $5 : 7, 14 : 10$ and $2 : 3$

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

  1. $2 : 3$

  2. $3 : 5$

  3. $7 : 8$

  4. $9 : 11$

Show answer
Correct Option: A
Explanation:

By the defination of compound ratio $5 : 7, 14 : 10$ and $2 : 3$ can be expressed as
$\dfrac {5}{7} \times \dfrac {14}{10}\times \dfrac {2}{3} = \dfrac {2}{3}$
Hence $2 : 3$

Find the compounded ratio of $l : m, m : n$ and $n : o$

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

  1. $l : n$

  2. $n : m$

  3. $l : o$

  4. $l : m$

Show answer
Correct Option: C
Explanation:

By the defination of compound ratio $l : m, m : n$ and $n : o$ can be expressed as
$\dfrac {l}{m}\times \dfrac {m}{n} \times \dfrac {n}{o} = \dfrac {l}{o}$
Hence $l : o$