Mathematics · Quantitative Aptitude

Ratios and Proportions

309 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

The ratio of the number of red pens in a bag to that of blue pens is 1 : 2. If 9 black pens are added, the ratio of the numbers of red, blue and black pens becomes 2 : 4 : 3. How many blue pens were in the bag

  1. 11

  2. 10

  3. 12

  4. 15

  5. N/A
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The ratio of red, blue and black pens is 2 : 4 : 3. The number of red, blue and black pens are 2x, 4x and 3x respectively. => 3 x = 9=> x = 3 Therefore the number of blue pens = 4 x = 4 x 3 = 12

Multiple choice

Compare 4/12 and 4/5

  1. <

  2. =

  3. >
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

4/12 simplifies to 1/3, which is approximately 0.33. 4/5 is 0.8. Since 0.33 < 0.8, 4/12 < 4/5.

Multiple choice conversion of time time conversion time measurement of time maths

State 'T' for true and 'F' for false.
(I) $12$ hours $:30$ hours $=8$km $:20$km
(II) The ratio of $1$ hour to one day is $1:1$
(III) The two terms of a ratio can be in two different units.

  1. (I)-T, (II)-T, (III)-T

  2. (I)-F, (II)-F, (III)-F

  3. (I)-T, (II)-F, (III)-F

  4. (I)-F, (II)-T, (III)-F
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$i)$ $12$ hours $:$ $30$ hours$=8Km:20Km$

$\cfrac{12}{30}=\cfrac{2}{5}$ hours.
$\cfrac{8}{20}=\cfrac{2}{5}$ Km.
Hence, $True.$
$ii)$ The ratio of $1$ hour to $1$ day,
$\cfrac{1\quad hour}{1\quad day}=\cfrac{1}{24}\quad hours\neq 1$
Hence, $false.$
$iii)$ The two terms of a ratio can not be in two different units.
Hence, $false$.
$(I)-T, (II)-F,(III)-F$

Multiple choice construction : division of a line segment dividing a line segment into three or five equal parts divsion of line segmet in given ratio constructions maths

A square sheet of paper $ABCD$ is so folded that $B$ falls on the mid point $M$ of $CD$. The crease will divide $BC$ in the ratio :

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

This is a geometry problem involving folding a square. Let the side be 2. B is (2,2), M is (1,0). The crease is the perpendicular bisector of BM. Solving for the intersection with BC gives the ratio.

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

If $\displaystyle \frac { a }{ b } -\frac { c }{ d } =0$ and bc=7, then determine the true statement among the following.

  1. a and b are directly proportional.

  2. a and c are inversely proportional.

  3. a and d are inversely proportional.

  4. b and c are directly proportional.

  5. c and d are inversely proportional.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\dfrac{a}{b}-\dfrac{c}{d}=0$

$\Rightarrow \dfrac{a}{b}=\dfrac{c}{d}$
$\Rightarrow ad=bc$
According to the question $bc=7$
$\therefore ad=7$
Then $a$ and $d$ are inversely proportional to eachother.

Multiple choice maths direct proportion and inverse proportion inverse proportion rule of three types of proportions

Which of the following are in inverse proportion?

  1. The number of workers on a job and the time to complete the job.

  2. The time taken for a journey and the distance travelled in a uniform speed.

  3. Area of cultivated land and the crop harvested.

  4. The time taken for a fixed journey and the speed of the vehicle.

  5. The population of a country and the area of land per person.
Reveal answer Fill a bubble to check yourself
A,D,E Correct answer
Explanation

Inverse proportion is a relation between two quantities such that one increases in proportion as the other decreases i.e. If $x$ increases as $y$ decreases, $x \alpha \dfrac{1}{y}$ 


In option A, if the no. of workers are increased then the time required to do the job will decrease, likewise if no. of workers decrease, then time to do the same job will increase i.e. no. of workers and time to do the job are inversely proportional to each other.


Similarly is the option D and E where the time taken to complete the journey is inversely proportional to the speed of vehicle and population is inversely proportional to area of the land respectively, are both examples of inverse proportion. 

So, the answer is A, D, E.

Multiple choice introduction to ratio and percentages comparing quantities maths

What is the sum of two numbers?
I. The bigger of these two numbers is 6 more than the smaller number.
II. 40% of the smaller number is equal to 30% of the bigger number.
III. The ratio between half of the bigger number and one-third of the smaller number is 2 : 1

  1. Only II and III are sufficient

  2. Only I and II are sufficient

  3. I and either II or III is sufficient

  4. All, II and III together are sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From the given statements we can make the following equations.
(I) $\Rightarrow y=x+6$
(II) $\Rightarrow 0.4x=0.2y\Rightarrow \frac {x}{y}=\frac {x}{y}=\frac {3}{4}$
(III) $\Rightarrow \frac {y/2}{x/3}=\frac {2}{1}\Rightarrow \frac {y}{x}=\frac {4}{3}\Rightarrow \frac {x}{y}=\frac {3}{4}$
Obviously, question can be solved by using (I) and either (II) or (III) because equations (II) and (III) are same.

Multiple choice maths direct proportion and inverse proportion rule of three types of proportions direct proportion

Observe the values and find the quantities which are in direct proportion
$ \begin{equation}x : \;\;[4\;\;6\;\;8\;\;10] \ y : \;\;[2\;\;3\;\;4\;\;\;5] \ z : \;\;[1\;\;2\;\;3\;\;\;4]\end{equation}$

  1. x & y

  2. y & z

  3. x & z

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By definition of direct proportion,

$a \  \alpha \  b$ i.e. $a = Kb$ where $K$ is constant of proportionality
$\therefore \dfrac{a}{b} = K$  ........ equation $1$

From given example, consider
$\dfrac{x}{y} =\dfrac{4}{2} = \dfrac{6}{3} = \dfrac{8}{4} = \dfrac{10}{5} = 2$

where as
$\dfrac{x}{z} = \dfrac{4}{1}\neq\dfrac{6}{2}\neq\dfrac{8}{3}\neq\dfrac{10}{4}$

$\therefore$ $x$ and $y$ obey the equation $1$

Hence $x$ and $y$ are in inverse proportion.
Answer is A

Multiple choice maths direct proportion and inverse proportion rule of three types of proportions direct proportion

Mark the correct alternative of the following.
Two numbers are in the ration $3 : 5$ and their sum is $96$. The larger number is?

  1. $36$
  2. $42$
  3. $60$
  4. $70$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given two numbers are  in the ratio $3:5$.

Let the numbers are $3x$ and $5x$.
Then according to the problem we get,
$3x+5x=96$
or, $8x=96$
or, $x=12$.
So the largest number is $12\times 5=60$.