Mathematics · Quantitative Aptitude

Ratios and Proportions

302 Questions

Ratios and proportions deal with comparing two or more quantities and finding their relationships. The questions involve calculating compound ratios, duplicate ratios, and solving proportional equations. This topic is a crucial part of the mathematics and quantitative aptitude sections in competitive exams.

compound ratiosduplicate ratiosproportion equationssimple ratio calculationscombining multiple ratios

Ratios and Proportions Questions

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

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

  1. $16:81$
  2. $4:9$
  3. $2:1$
  4. $12:81$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 =$\left ( \dfrac{4/9}{2/3} \right )^{2}=4:9$

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

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

  1. $1 : 3$
  2. $4 : 5$
  3. $5 : 4$
  4. $3 : 1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

  1. $36 : 25$
  2. $\dfrac {1}{5} : \dfrac {1}{6}$
  3. $25 : 36$
  4. $30 : 15$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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

  1. $16 : 64$
  2. $9 : 64$
  3. $16 : 81$
  4. $1 : 36$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $(1)^{2} : (6)^{2} = 1 : 36$.

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

If $a : b = 2 : 3$ and $b : c = 9 : 8$ then the duplicate ratio of $a : c$ is ____

  1. $9 : 16$
  2. $4 : 9$
  3. $81 : 64$
  4. $4 : 64$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$a : b = 2 : 3$
$b : c = 9 : 8$
$\therefore \dfrac {a}{b} \times \dfrac {b}{c} = \dfrac {2}{3} \times \dfrac {9}{8}$
$\therefore \dfrac {a}{c} = \dfrac {3}{4} \Rightarrow a : c = 3 : 4$.
$\therefore$ The duplicate ratio of $3 : 4$ is $3^{2} : 4^{2} = 9 : 16$

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

If $(5x + 3) : (3x + 1)$ is the triplicate ratio of $4 : 3$, then $x =$ _____

  1. $57$
  2. $17$
  3. $\dfrac {17}{57}$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The triplicate ratio of $4 : 3$ is $4^{3} : 3^{3}$
$\therefore \dfrac {5x + 3}{3x + 1} = \dfrac {64}{27}$
$\Rightarrow 135x + 81 = 192x + 64$
$\Rightarrow 192x - 135x = 81 - 64$
$\Rightarrow 57x = 17$
$\therefore x = \dfrac {17}{57}$

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

If $x : y = 2 : 5, y : z = 15 : 8$ and $z : w = 3 : 2$, then find the triplicate ratio of $x : w$

  1. $\sqrt [3]{9} : \sqrt [3]{8}$
  2. $3 : 4$
  3. $729 : 512$
  4. $81 : 64$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$x : y = 2 : 5, y : z = 15 : 8, z : w = 3 : 2$
$\therefore \dfrac {x}{y}\times \dfrac {y}{z}\times \dfrac {z}{w} = \dfrac {2}{5} \times \dfrac {15}{8}\times \dfrac {3}{2} = \dfrac {9}{8}$
$\therefore x : w = 9 : 8$
$\therefore$ The triplicate ratio of $9 : 8$ is $9^{3} : 8^{3} = 729 : 512$

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

The subduplicate ratio of $9 : 1$ is $(x + y) : (x - y)$. Then $x : y =$ _____

  1. $2 : 1$
  2. $1 : 2$
  3. $4 : 3$
  4. $6 : 4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The subduplicate ratio of $9 : 1$ is $\sqrt {9} : \sqrt {1} = 3 : 1$
$\therefore \dfrac {x + y}{x - y} = \dfrac {3}{1} \Rightarrow x + y = 3x - 3y$
$\Rightarrow 2x = 4y \Rightarrow \dfrac {x}{y} = \dfrac {4}{2} = \dfrac {2}{1}$

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

The triplicate ratio of $(x + y)^{\frac {2}{3}} : (x - y)^{\frac {2}{3}}$ is _____

  1. $(x + y)^{2} : (x - y)^{2}$
  2. $(x + y) : (x - y)$
  3. $(x + y)^{3} : (x - y)^{3}$
  4. $(x + y)^{6} : (x - y)^{6}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The triplicate ratio of $a : b$ is $a^{3} : b^{3}$
$\therefore$ The triplicate ratio of $(x + y)^{\frac {2}{3}} : (x - y)^{\frac {2}{3}}$ is $[(x + y)^{\frac {2}{3}}]^{3} : [(x - y)^{\frac {2}{3}}]^{3}$
$= (x + y)^{2} : (x - y)^{2}$

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

The subduplicate ratio of $(x^{2} - y^{2})^{2} : (x + y)^{2}$ is _____

  1. $x^{2} - y^{2} : 1$
  2. $x - y : 1$
  3. $x + y : 1$
  4. $1 : x + y$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\dfrac {(x^{2} - y^{2})^{2}}{(x + y)^{2}} = \dfrac {((x - y)(x + y))^{2}}{(x + y)^{2}} = \dfrac {(x - y)^{2}}{1}$
$\therefore$ The subduplicate ratio of $(x - y)^{2} : 1$ is $\sqrt {(x - y)^{2}} : \sqrt {1} = (x - y) : 1$.