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

What is the compounded ratio of $(a - b) : (a + b), (a - b)^{2} : (a + b)^{2}$ and $(a + b)^{3} : (a - b)^{3}$

  1. $8 : 9$
  2. $5 : 7$
  3. $1 : 1$
  4. $3 : 5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By the defination of compound ratio these ratio can be expressed as
$\dfrac {a - b}{a + b}\times \dfrac {(a - b)^{2}}{(a + b)^{2}} \times \dfrac {(a + b)^{3}}{(a - b)^{3}} = \dfrac {1}{1}$
Hence, $1 : 1$.

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

The sub-duplicate ratio of $9a^{2}b^{2} : 16r^{2} s^{2}$ is _____

  1. $3a : 4r$
  2. $4ab : 3rs$
  3. $3ab : 4rs$
  4. $3b : 4s$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sub-duplicate ratio of $x : y$ is $\sqrt {x} : \sqrt {y}$
$\therefore$ The subduplicate ratio of $9a^{2}b^{2} : 16r^{2}s^{2}$ is $\sqrt {9a^{2}b^{2}} : \sqrt {16r^{2}s^{2}}$
$= 3ab : 4rs$

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

The sub-duplicate ratio of $\dfrac {1}{25} : \dfrac {1}{64}$ is _____

  1. $\dfrac {1}{5} : \dfrac {1}{8}$
  2. $5 : 4$
  3. $\dfrac {1}{125} : \dfrac {1}{252}$
  4. $1 : 1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The subduplicate ratio of $a : b$ is $\sqrt {a} : \sqrt {b}$
$\therefore$ The subduplicate ratio of $\dfrac {1}{25} : \dfrac {1}{64}$ is $\sqrt {\dfrac {1}{25}} : \sqrt {\dfrac {1}{64}} = \dfrac {1}{5} : \dfrac {1}{8}$

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

The triplicate ratio of $ab^{\frac {2}{3}} : a^{\frac {2}{3}}b$ is _____

  1. $1 : 1$
  2. $ab : 1$
  3. $a^{3}b^{2} : a^{2}b^{3}$
  4. $a : b$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The triplicate ratio of $ab^{\frac {2}{3}} : a^{\frac {2}{3}} b$ is $(ab^{\frac {2}{3}})^{3} : (a^{\frac {2}{3}}b)^{3}$
$= a^{3} \cdot b^{2} : a^{2}b^{3}$
$a^{3}b^{2} : a^{2}b^{3} = \dfrac {a^{3}b^{2}}{a^{2}b^{3}} = \dfrac {a}{b}$

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

The subtriplicate ratio of $125y^{3} : 1000z^{6}$ is ____

  1. $5y : 10z^{3}$
  2. $5y : 10z^{2}$
  3. $1000z^{6} : 125y^{3}$
  4. $10^{3} : 5y$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The subtriplicate ratio of $a : b$ is $\sqrt [3]{a} : \sqrt [3]{b}$.
$\therefore$ The subtriplicate ratio of $125y^{3} : 1000z^{6}$ is $\sqrt [3]{125y^{3}} : \sqrt [3]{1000z^{6}} = 5y : 10z^{2}$.

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

The subtriplicate ratio of $64m^{6} : 27n^{3}$ is ____

  1. $27n^{3} : 64 m^{6}$
  2. $4m : 3n$
  3. $4m^{2} : 3n$
  4. $4m^{3} : 3n$
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 $64 m^{6} : 27 n^{3}$ is $\sqrt [3]{64m^{6}} : \sqrt [3]{27n^{3}}$
$= 4m^{2} : 3n$

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

_____ is the sub-duplicate ratio of $\dfrac {1}{46} : \dfrac {1}{36}$

  1. $\dfrac {1}{4} : \dfrac {1}{6}$
  2. $\dfrac {1}{2} : \dfrac {1}{6}$
  3. $\dfrac {1}{6} : \dfrac {1}{2}$
  4. $\dfrac {1}{16} : \dfrac {1}{216}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The subduplicate ratio of $\dfrac {1}{4} : \dfrac {1}{36}$ is $\sqrt {\dfrac {1}{4}} : \sqrt {\dfrac {1}{36}} = \dfrac {1}{2} : \dfrac {1}{6}$