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 maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Divide 170 into three parts such that the first part is 10 more than the second and its ratio with the third part is 2:5.

  1. $40, 30, 100$
  2. $20, 30, 100$
  3. $40, 50, 100$
  4. $50, 30, 100$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the first part =x. Then,
Second part = x-10
$\displaystyle \frac {First \ part}{Third \ part} = \frac {2}{5} \Rightarrow Third \ part = \frac {5x}{2} $
Given, $ \displaystyle x= x - 10 + \frac {5x}{2}= 170 \Rightarrow 2x+ 2x - 20 + 5x = 340 \Rightarrow 9x = 360 \Rightarrow x = 40$
$\displaystyle \therefore $ The  three  parts  are  40, 40- 10 , 5 $ \displaystyle \times \frac {40}{2}$, i.e. , 40, 30, 100

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

In the word MATHEMATICS , the ratio of number of consonants to the number of vowels is _____ .

  1. $4 : 7$
  2. $7 : 4$
  3. $5 : 6$
  4. $6 : 5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  Consonants in the given word are = $M,T,H,M,T,C,S$

$\therefore$  Total number of consonants = $7$
$\Rightarrow$  Vowels in the given words are = $A,E,A,I$
$\therefore$  Total number of vowels = $4$.

$\therefore$  $\dfrac{Number\,of\,consonants}{Number\,of\,viwels}=\dfrac{7}{4}$

$\therefore$   Required ratio is $7:4$

Multiple choice physics simple machine common machines terms related to machines introduction to simple machines

Fill in the blank.
In the first order of lever, velocity ratio is usually __than 1 but could be __ or equal to 1

  1. greater, less

  2. less, more

  3. greater, more

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

In a first-class lever, the fulcrum position can be adjusted. If the effort arm is longer than the load arm, the mechanical advantage (and velocity ratio) is greater than 1; if shorter, it is less than 1; if equal, it is 1.

Multiple choice chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

If two masses A and B have their masses in the ratio 1 : 4 and their volumes are equal, then their densities have the ratio

  1. 1:4

  2. 8:1

  3. 2: 4

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

Let mass of $A$ be $m$

Mass of $B$ be $4m$
Let density of $A$ be $d _a$
Density of $B$ be $d _b$
And Volume of A$=$Volume of B$=V$
As Density$=\dfrac{\text {Mass}}{\text {Volume}}$

Therefore $d _a=\dfrac{m}{V}$
$d _b=\dfrac{4m}{V}$

$\dfrac{d _a}{d _b}=\dfrac{\dfrac{m}{V}}{\dfrac{4m}{V}}$
$\dfrac{d _a}{d _b}=\dfrac{m}{4m}=\dfrac{1}{4}$
Hence the correct answer is option (A).

Multiple choice chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

The ratio of the values in SI units to values in CGS units of density is

  1. $10^3:1$
  2. $10^2:1$
  3. $10^{-2}:1$
  4. $10^{-3}:1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

the density of water in S.I. unit $\rho=1000 kg/{m}^3$

the density of water in CGS unit $\rho'=1 gm/cc$

the ratio of the densities of water in the different system 
$\dfrac{\rho}{\rho'}=\dfrac{{10}^3}{1}$

Multiple choice chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

If two masses A and B have their masses in the ratio 1 : 4 and their volumes are equal, then their densities have the ratio :

  1. 1 : 4

  2. 4 : 1

  3. 2 : 1

  4. 3 : 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
We know that density is defined as:
$\rho=\dfrac{mass}{volume}$

It means that density is directly proportional to the mass.
$\dfrac{d}{d'}=\dfrac{m}{m'}=\dfrac14$

Since, $m:m'=1:4$

$\therefore, d:d'=1:4$
Multiple choice botany nucleus and chromosome membrane bound organelles cell: size and differentiation microscopy

Arm ratio in metacentric condition is

  1. 1:1

  2. 1:2

  3. 1:3

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

The arm ratio in metacentric condition is 1:1. These are X-shaped chromosomes, with the centromere in the middle, so that, the two arms of the chromosomes are almost equal. A chromosome is metacentric, if its two arms are roughly equal in length. In a normal human karyotype, two chromosomes are considered metacentric: chromosomes 1 and 3. In some cases, a metacentric chromosome is formed by balanced translocation: the fusion of two acrocentric chromosomes to form one metacentric chromosome.

Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

Divide $Rs\ 1,545$ between three people $A,B$ and $C$ such that $A$ gets three-fifths of what $B$ gets and the ratio of the share of $B$ to $C$ is $6:11$.
what amount will each person get ?

  1. $A=240, \ B= 440, \ C=825$
  2. $A=230, \ B= 440, \ C=825$
  3. $A=270, \ B= 450, \ C=825$
  4. $A=245, \ B= 440, \ C=825$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$3\times \dfrac {6x}{5}+6x+11x=1545$
$\dfrac {18x+30x+55x}{5}=1545$
$\dfrac {103x}{5}=1545$
$x=\dfrac {5\times 1545}{103}$
$x=75$
$A=\dfrac {18}{5}\times 75 =270$
$B=6\times 75 =450$
$C=11\times 75=825$


Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

if $76$ is divided into four parts proportional to $7,5,3.4$ then the smallest part is:

  1. $12$
  2. $15$
  3. $16$
  4. $19$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Four parts proportional to 

$7,5,3$ and $4$

$\therefore $  Four part are equal to$7x, 5x, 3x,$ and $4x.$

$\therefore7x+5x+3x+4x=76$

$\therefore 19x=76$

$\therefore x=\dfrac {76}{19}$

$\therefore x=4$

$\therefore 7x=4\times7=28$

$\therefore 5x=5\times4=20$

$\therefore 3x=3\times 4=12$

$\therefore 4x=4\times4=16$

$\therefore $ For parts are $28, 20, 12$ and $16$.
Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

Division of numbers is performed when we ________ certain quantities.

  1. Distribute

  2. Share

  3. Divide

  4. Add
Reveal answer Fill a bubble to check yourself
A,B,C Correct answer
Explanation
Division is splitting into equal parts or groups. It is the result of "fair sharing".
Example: there are $12$ chocolates, and $3$ friends want to share them, how do they divide the chocolates?
Answer: They should get $4$ each.

We use the ÷ symbol, or sometimes the / symbol to mean divide:
$12 ÷ 3 = 4$
$12 / 3 = 4$