Tag: composition of ratios

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Questions Related to composition of ratios

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

If $x : y = 1 : 2$ and $y : z = 8 : 3$, then the reciprocal ratio of $z : x$ is ____

  1. $3 : 8$

  2. $1 : 3$

  3. $3 : 4$

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

$x : y = 1 : 2$ and $y : z = 8 : 3$
$\therefore x : z = \dfrac {x}{y} \times \dfrac {y}{z} = \dfrac {1}{2} \times \dfrac {8}{3} = \dfrac {4}{3} = 4 : 3$
Now, the reciprocal ratio of $z : x$ is $x : z$
$\therefore x : z = 4 : 3$

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

The subtriplicate ratio of $(x^{4} - y^{4})^{3} : (x^{2} + y^{2})^{6}$ is ____

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

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

  3. $(x - y) : (x + y)$

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

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
$\therefore$ The subtriplicate ratio of $(x^{4} - y^{4})^{3} : (x^{2} + y^{2})^{6}$ is $\sqrt [3]{(x^{4} - y^{4})^{3}} : \sqrt [3]{(x^{2} + y^{2})^{6}} = (x^{4} - y^{4}) : (x^{2} + y^{2})^{2}$
$= \dfrac {x^{4} - y^{4}}{(x^{2} + y^{2})^{2}} = \dfrac {(x^{2} - y^{2})(x^{2} + y^{2})}{(x^{2} + y^{2})^{2}}$
$= \dfrac {x^{2} - y^{2}}{x^{2} + y^{2}} = x^{2} - y^{2} : x^{2} + y^{2}$

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

If $a : b = 2 : 3$ and $b : c = 4 : 7$ then the reciprocal ratio of $a : c$ is ____

  1. $8 : 21$

  2. $21 : 8$

  3. $7 : 4$

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

$a : b = 2 : 3$ and $b : c = 4 : 7$
$\therefore a : c = \dfrac {a}{b} \times \dfrac {b}{c} = \dfrac {2}{3} \times \dfrac {4}{7}$
$= \dfrac {8}{21}$
$\therefore a : c = 8 : 21$
$\therefore$ The reciprocal ratio of $a : c$ is $21 : 8$.

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

_____ is the subtriplicate ratio of $(a + b)^{3} : (a^{2} - b^{2})^{3}$

  1. $(a + b) : 1$

  2. $1 : (a + b)$

  3. $1 : (a - b)$

  4. $(a - b) : 1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$
$\therefore$ The subtriplicate ratio of $(a + b)^{3} : (a^{2} - b^{2})^{3}$ is $\sqrt [3]{(a + b)^{3}} : \sqrt [3]{(a^{2} - b^{2})^{3}} = (a + b) : (a^{2} - b^{2})$
$= \dfrac {a + b}{a^{2} - b^{2}} = \dfrac {a + b}{(a - b)(a + b)} = \dfrac {1}{a - b} = 1 : (a - b)$.