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 law of reciprocal proportion laws of chemical combination basic concepts of chemistry some basic concepts of chemistry chemistry

The weight ratio of two elements A and B which combine with the fixed weight of C separately is either the same or some simple whole number multiple of the weight ratio in which A and B combine together. This statement explains :

  1. law of multiple proportion.

  2. law of reciprocal proportion.

  3. law of conservation of mass.

  4. law of constant composition.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The weight ratio of two elements A and B which combine with the fixed weight of C separately is either the same or some simple whole number multiple of the weight ratio in which A and B combine together. This statement explains the Law of reciprocal proportion.
For example, 23 g of $Na$ combines with 35.5 g of $Cl$ and 1 g of $H$ to form $NaCl$ and $NaH$. Hence, 35.5 g of $Cl$ and 1 g of $H$ will combine to form $HCl$.

Multiple choice statistics measures of central tendency geometric and harmonic mean geometric mean mean

Find the sum of 5 geometric means between $\displaystyle\frac{1}{3}$ and 243, by taking common ratio positive.

  1. 121

  2. 126

  3. 81

  4. 111
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given that, there are $5$geometric means between the two numbers $\dfrac{1}{3}$and $243$ , we have to find $7=\left( 5+2 \right)$

terms in G.P. of which $\dfrac{1}{3}$ is the first, and$243$ the seventh. Let r be the common ratio;

then $243$  = the seventh term =$\left( \dfrac{1}{3} \right){{r}^{\left( 7-1 \right)}}=\dfrac{1}{3}.{{r}^{6}}$.

 

Therefore,${{r}^{6}}=3.x.243={{3.3.3}^{4}}={{3}^{6}}$;

whence $r=6$

and the series is$\dfrac{1}{3},1,3,9,27,81,243$

(using the standard form a, ar, ar², ar³ …… of a G.P. ).

 

Now, the geometric mean between two given quantities$a,b=\sqrt{ab}$

 

Therefore, the required geometric means are,

$ \sqrt{\dfrac{1}{3}.x.3},\sqrt{1.x.9},\sqrt{3.x.27},\sqrt{9.x.82},\sqrt{27.x.243} $$

$ =1,3,9,27,81 $$

 

Therefore, the sum of the $5$  geometric means is

$1+3+9+27+81=121$

 

Hence, this is the answer.

 

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 mid-point and its converse application of the mid-point theorem mid point theorem mid-point theorem and its converse

Suppose $ABCD$ is a rhombus. A straight line passing through $C$ meet $AD$ which is produced at $P$ and meet $AB$ produced at $Q$. Therefore if $DP=\dfrac {1}{2}AB$, then find the ratio between $BQ$ and $AB$?

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

$ ABCD $ is a rhombus. $ AB =BC = CD = DA $


$ \displaystyle \frac{DP}{AB} = \frac{1}{2} \Rightarrow DP =1 AB =2 $

In rhombus  $ \angle \theta _1 = \angle \theta _2 $

$ \angle Q $ is common for the $ \triangle BCQ \, and \, \triangle APQ $

$ \because \angle APQ = \angle BCQ $

$ \because \triangle BCQ $ is similar to $ \triangle APQ $ by $ AAA $ property. 

$ \displaystyle \frac{AP}{BC} = \frac{AQ}{BQ} = \frac{AD + DP}{BC} = \frac{3}{2} $

$ \displaystyle \frac{AQ}{BQ} = \frac{3}{2} \Rightarrow \frac{AB + BQ}{BQ} = \frac{3}{2} $

$ \displaystyle \frac{AB}{BQ} = \frac{3}{2} - 1 = \frac{1}{2} $

$ \displaystyle \frac{BQ}{AB} = \frac{2}{1} $

Multiple choice trihybrid cross classical genetics botany

Trihybrid ratio is

  1. 27 : 9 : 9 : 9 : 3 : 3 : 3 : 1

  2. 27 : 9 : 9 : 6 : 6 : 3 : 3 : 1

  3. 1 : 6 : 15 : 20 : 15 : 6 : 1

  4. 36 : 6 : 6 : 6 : 3 : 3 : 3 : 1.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A cross is made between the two parents on the basis of 3 contrasting characters is called Trihybrid cross. Mendel conducted trihybrid cross by three characters height of the stem, form of seed, and colour of the cotyledons. In the F2 generation, he obtained, 27:9:9:9:3:3:3:1.

So, the correct option is ‘27:9:9:9:3:3:3:1’.

Multiple choice mean and median mean maths assumed mean method assumed mean method of finding mean measure of central tendency

Three geometric means between 5 and 3125 are___.

  1. 15,75,375

  2. 25,125,625

  3. 11,44,176

  4. 10,40,160
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The geometric mean is a geometric series which is in the form of arn where a is the first term and r is the common ratio.

T1= 5 and T5 = 3125

Now, T1/T5 = 5/ 3125

=>ar1//ar5 =1/ 625

=> 1/ r4 = 1/625

=> r4 = 625

=> r = 5

So if r=5, then a= 1

T2 = ar2

      = 1(5) 2 = 25

T3 = ar3

      = 1(5) 3 = 125

T4 = ar4

      = 1(5)4 = 625

Therefore, three geometric means between 5 and 3125 are 25, 125 and 625. 

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 $12\times 5=60$.