Tag: maths

Questions Related to maths

What is the reciprocal ratio of $8 : 15$?

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

  1. $225 : 64$

  2. $16 : 30$

  3. $64 : 225$

  4. $15 : 8$

Show answer
Correct Option: D
Explanation:

The reciprocal ratio of $a : b$ is $b : a$
$\therefore$ reciprocal ratio of $8 : 15$ is $15 : 8$

What is the reciprocal ratio of $(x - 5) : (x - 7)$

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

  1. $(x + 5) : (x + 7)$

  2. $(x + 7) : (x + 5)$

  3. $(x + 14) : (x + 28)$

  4. $(x - 7) : (x - 5)$

Show answer
Correct Option: D
Explanation:

The reciprocal ratio of $a : b$ is $b : a$
$\therefore$ reciprocal ratio of $(x - 5) : (x - 7)$ is $(x - 7) : (x - 5)$

What is the reciprocal ratio of $(x + 12) : (x + 21)$?

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

  1. $(x + 21) : (x + 12)$

  2. $(x + 24) : (x + 42)$

  3. $(x + 6) : (x + 10)$

  4. $(x + 42) : (x + 24)$

Show answer
Correct Option: A
Explanation:

The reciprocal ratio of $a : b$ is $b : a$
$\therefore$ reciprocal ratio of $(x + 12) : (x + 21)$ is $(x + 21) : (x + 12)$

The ratio compound of $2:3$ and sub-duplicate ratio of $4:9$ is __________.

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

  1. $16:81$

  2. $4:9$

  3. $2:1$

  4. $12:81$

Show answer
Correct Option: B
Explanation:

we have to find the ratio compound of $2:3$ and sub-duplicate ratio of $4:9$ 

The duplicate ratio of $a:b$ is also called compound ratio of $a:b$ and is equal to $a^{2}:b^{2}$
 Similarly, sub-duplicate ratio of  $a:b$ is $\sqrt{a}:\sqrt{b}$  
Therefore compound ratio of $2:3=4:9$ 
Sub-duplicate ratio of $4:9=\sqrt{4}:\sqrt{9}=2:3$
 Ratio compound =$\left ( \dfrac{4/9}{2/3} \right )^{2}=4:9$

What is the reciprocal ratio of $21 : 31$?

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

  1. $42 : 62$

  2. $62 : 42$

  3. $35 : 37$

  4. $31 : 21$

Show answer
Correct Option: D
Explanation:

The reciprocal ratio of $a : b$ is $b : a$
$\therefore$ reciprocal ratio of $21 : 31$ is $31 : 21$

The value of $x : y$ is _____, if $(4x + 7y) : (5x - y)$ is the duplicate ratio of $5 : 1$

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

  1. $32 : 121$

  2. $25 : 1$

  3. $1 : 5$

  4. $1 : 25$

Show answer
Correct Option: A
Explanation:

$(4x + 7y) : (5x - y)$ is the duplicate ratio of $5 : 1$.
Also, the duplicate ratio of $5 : 1$ is $25 : 1$.
$\therefore \dfrac {4x + 7y}{5x - y} = \dfrac {25}{1}\Rightarrow 4x + 7y = 125x - 25y$
$\therefore 125x - 4x = 7y + 25y$
$\therefore 121x = 32y$
$\therefore \dfrac {x}{y} = \dfrac {32}{121}$
$\therefore x : y = 32 : 121$

If $(x + y) : (x - y)$ is equal to the duplicate ratio of $3 : 1$, then $x : y = $ _____

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

  1. $1 : 3$

  2. $4 : 5$

  3. $5 : 4$

  4. $3 : 1$

Show answer
Correct Option: C
Explanation:

The duplicate ratio of $a : b$ is $a^{2}:b^{2}$
$\therefore$ The duplicate ratio of $3 : 1$ is $9 : 1$.
$\therefore \dfrac {x + y}{x - y} = \dfrac {9}{1}$
$\therefore x + y = 9x - 9y$
$\therefore y + 9y = 9x - x$
$\therefore 10y = 8x$
$\therefore \dfrac {x}{y} = \dfrac {10}{8} = \dfrac {5}{4}$
$\therefore x : y = 5 : 4$.

The value of $x$ is ____ if $(3x + 1) : (5x - 4)$ is the duplicate ratio of $5 : 6$

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

  1. $2$

  2. $4$

  3. $8$

  4. $6$

Show answer
Correct Option: C
Explanation:

$(3x + 1) : (5x - 4)$ is the duplicate ratio of $5 : 6$.
Also, the duplicate ratio of $5 : 6$ is $5^{2} : 6^{2} = 25 : 36$
$\therefore \dfrac {3x + 1}{5x - 4} = \dfrac {25}{36}$
$\therefore 108 x + 36 = 125x - 100$
$\therefore 125x - 108x = 36 + 100$
$\therefore 17x = 136$
$\therefore x = \dfrac {136}{17} = 8$

The duplicate ratio of $\dfrac {1}{6} : \dfrac {1}{5}$ is ____

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

  1. $36 : 25$

  2. $\dfrac {1}{5} : \dfrac {1}{6}$

  3. $25 : 36$

  4. $30 : 15$

Show answer
Correct Option: C
Explanation:

The duplicate ratio of $a : b$ is $a^{2} : b^{2}$
$\therefore$ The duplicate ratio of $\dfrac {1}{6} : \dfrac {1}{5}$ is $\left (\dfrac {1}{6}\right )^{2} : \left (\dfrac {1}{5}\right )^{2} = \left (\dfrac {1}{36}\right ) : \left (\dfrac {1}{25}\right )$
$= \dfrac {\dfrac {1}{36}}{\dfrac {1}{25}} = \dfrac {25}{36}$.

If $x : y = 4 : 9$ and $y : z = 3 : 8$, then the duplicate ratio of $x : z$ is ____

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

  1. $16 : 64$

  2. $9 : 64$

  3. $16 : 81$

  4. $1 : 36$

Show answer
Correct Option: D
Explanation:

$x : y = 4 : 9$
$y : z = 3 : 8$
$\therefore \dfrac {x}{y} \times \dfrac {y}{z} = \dfrac {4}{9}\times \dfrac {3}{8}$
$\therefore \dfrac {x}{z} = \dfrac {1}{6}\Rightarrow x : z = 1 : 6$
$\therefore$ The duplicate ratio of $x : z$ is $(1)^{2} : (6)^{2} = 1 : 36$.