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

A sum of money is divided into $2$ parts such that $6$ times of one part added to $15$ times the other gives $8$ times the whole. What is the ratio of one part to the other?

  1. $5 : 2$
  2. $4 : 9$
  3. $7 : 6$

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

Let two parts of money  be Rs. $ x$ and Rs. $ y$.
Then, according to the given condition,

$\Rightarrow 6x+15y=8(x+y)$
$\Rightarrow 6x+15y=8x+8y$
$\Rightarrow 2x=7y$
$\Rightarrow \displaystyle \frac{x}{y}=\frac{7}{2}$
$\Rightarrow  x:y=7:2$

Hence, option D.

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

Divide $Rs.\,715$ in the ratio $\displaystyle\frac{1}{2}\colon\displaystyle\frac{1}{3}\colon\displaystyle\frac{1}{4}$.

  1. $\;Rs.\,350,\,Rs.\,250,\,Rs.\,115$
  2. $\;Rs.\,300,\,Rs.\,250,\,Rs.\,165$
  3. $\;Rs.\,330,\,Rs.\,220,\,Rs.\,165$
  4. $\;Rs.\,400,\,Rs.\,260,\,Rs.\,55$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The ratio in which Rs $715$ is to be divided is $6:4:3$.

So, we have $13x = 715$ or $x = 55$
So, $6x$ will be Rs. $330$
$3x$ will be Rs $165$ and $4x$ is Rs $220$.

So, the answer is option $C$

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

An amount of money is to be distributed among $A,B\,$and$\,C$ in the ratio $3\,\colon\,1\,\colon\,5$. The difference between $B's$ share and $C's$ share is $Rs.\,3600$. What is the total of $A's$ share and $B's$ share?

  1. $\;Rs.\,5400$
  2. $\;Rs.\,3600$
  3. $\;Rs.\,2700$
  4. $\;Rs.\,1800$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the shares of $A,B\,$and$\,C$ be $3x,x\,$and$\,5x$ respectively.
$\;\;\;\;\;\;\;$ Given, $5x-x=3600\;\;\;\;\;\Rightarrow\;4x=3600$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\Rightarrow\,x=900$
$\;\;\;\;\;\;\;\;\therefore\;A's\;share+B's\;share=Rs.\,3\times900+Rs.\,900$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=Rs.\,2700+Rs.\,900$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\,Rs.\,3600$

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

Three numbers are in the ratio $\displaystyle\frac{1}{2}\colon\displaystyle\frac{2}{3}\colon\displaystyle\frac{3}{4}$. The difference between the greatest and the smallest numbers is $36$. The numbers are

  1. $\;72,84,108$
  2. $\;60,72,96$
  3. $\;72,84,96$
  4. $\;72,96,108$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The three numbers are in the ratio $\displaystyle\frac{1}{2}\colon\displaystyle\frac{2}{3}\colon\displaystyle\frac{3}{4}$,
$\;\;\;\;\;\;\;\;i.e.,\displaystyle\frac{1}{2}\times12\colon\displaystyle\frac{2}{3}\times12\colon\displaystyle\frac{3}{4}\times12,i.e.,\,6\,\colon8\,\colon\,9$.
$\;\;\;\;\;\;\;\;\;$ Let the number be $6x,8x$ and $9x$.
$\;\;\;\;\;\;\;\;\;$ Given, $9x-6x=36$
$\;\;\;\;\;\;\;\;\;\Rightarrow\,3x=36\;\Rightarrow\;x=12$
$\therefore$The numbers are $72,96$ and $108$.

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

A certain sum of money is divided between $P$ and $Q$ in the ratio $3\displaystyle\frac{1}{2}\,\colon\,5\displaystyle\frac{1}{2}$. If $P$ gets $Rs.\,180$ less than $Q$, then what is the share of $Q$?

  1. $\;Rs.\,315$
  2. $\;Rs.\,495$
  3. $\;Rs.\,630$
  4. $\;Rs.\,810$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Q's share be Q, and P's share be $(Q - 180)$


P : Q is $7 : 11$

    $\dfrac { Q -  180 }{ Q } =\dfrac { 7 }{ 11 } $
$11Q - 1980=\quad 7Q$
               $ 4Q= 1980$
                 $Q = 495$

So, Q is Rs $495$.

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

In a particular type of fertilizer, the ratio of two chemicals $A$ and $B$ is $2\,\colon\,5$. In $21:kg$ of this fertilizer, if $3:kg$ of $A$ is added. What will be the ratio of $A$ to $B$ in the new fertilizer?

  1. $\;1\,\colon\,1$
  2. $\;2\,\colon\,3$
  3. $\;3\,\colon\,5$
  4. $\;4\,\colon\,5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity of $A=\displaystyle\frac{2}{7}\times21:kg=6:kg$,
$\;\;\;\;\;\;\;$ Quantity of $B=\displaystyle\frac{5}{7}\times21:kg=15:kg$
$\;\;\;\;\;\;\;$ After adding $3:kg$ of $A$ in the given fertilizer,


$\;\;\;\;\;\;\;$ Required ratio $=\displaystyle\frac{Quantity\;of\;A}{Quantity\;of\;B}$

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\displaystyle\frac{(6+3):kg}{15:kg}=\displaystyle\frac{9}{15}=3\,\colon\,5$. 

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

Two numbers are in the ratio $2\,\colon\,3$. If $2$ is subtracted form the first and $2$ is added to the second, the ratio becomes $1\,\colon\,2$. What is the sum of the number?

  1. $\;30$
  2. $\;28$
  3. $\;24$
  4. $\;10$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two numbers be $2x$ and $3x$. Then,
$\;\;\;\;\;\;\;\;\displaystyle\frac{2x-2}{3x+2}=\displaystyle\frac{1}{2}\;\Rightarrow\;4x-4=3x+2\;\Rightarrow\,x=6$
$\therefore$ The numbers are $12$ and $18$.
Required sum$=12+18=30$.

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

The sum of three numbers is $116.$ The ratio of the second to the third is $9 : 16$ and the first to third is $1 : 4.$ The second number is

  1. $30$
  2. $32$
  3. $34$
  4. $36$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the 1st number be $x$. Then, third number $= 4x$
Given, $\displaystyle \frac{\text{2nd number}}{\text{3rd number}} = \frac{9}{16} \Rightarrow \frac{\text{2nd number}}{4x} = \frac{9}{16}$
$\Rightarrow \displaystyle \text{2nd number} = \frac{9}{16} \times 4x = \frac{9}{4} x$
Given, $\displaystyle x + \frac{9x}{4} + 4x = 116$
$\Rightarrow 4x + 9x + 16x = 116 \times 4$
$\Rightarrow 29 x = 116 \times 4 \Rightarrow x = \displaystyle \frac{116 \times 4}{29} = 16$
$\therefore \text{2nd number}= \displaystyle \frac{9}{16} \times 4 \times 16 = 36$

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

$Rs. 366$ is divided among A,B & C so that A get $\dfrac{1}{2}$ as much B & C together, B get $\dfrac{2}{3}$ as much A & C together , then the share of A is

  1. Rs. $122$
  2. Rs. $129.60$
  3. Rs. $146.60$
  4. Rs. $183$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$A:\begin{pmatrix}B+C\end{pmatrix}=1:2$
A"s share $=Rs.\dfrac{366\times1}{3}=Rs.122$

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

A sum of money is delivered among $A, B, C$ and $D$ in the ratio $3:4:9:10$. If the share of $C$ is Rs. $2580$ more than the share of $B$, What is the total amount of money of $A$ and $D$ together ?

  1. 6400

  2. 6708

  3. 6700

  4. 6510
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given ratio : $3 : 4 : 9 : 10$
Let $A$ share $= 3x$
$B$ share $= 4x$
$C$ share $= 9x$
$D$ share $ = 10x$
Given, $C$ share is $2580$ more than $B$ share i.e.
$9x - 2580 = 4x$
$5x = 2580$
$x = 516$
So, $A$ share $= 3x = 516\times 3 = 1548$
$D$ share  $= 10x = 516\times 10 = 5160$
$A + D = 1548 + 5160 =$ Rs. $6708$

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

$Rs. 2430$ are distributed among three persons so that their shares be diminished by $Rs. 5, Rs. 10$ and $Rs. 15$ respectively, the remainder shall be in the ratio $3 : 4 : 5.$ The share of $C$ is

  1. $Rs. 1015$
  2. $Rs. 605$
  3. $Rs. 810$
  4. $Rs. 1415$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let $Rs. 2430$ be divided among three persons with their shares as $x, y$ and $z$ respectively so that $x + y + z = 2430$
Given, $x - 5 : y - 10 : z - 15 = 3 : 4 : 5$
$\Rightarrow x- 5 = 3k, y - 10 = 4k $ and $ z - 15 = 5 k$
$\Rightarrow x = 3k + 5, y = 4k + 10$ and $z = 5k + 15$
$\therefore 3k + 5 + 4k + 10 + 5k + 15 = 2430$
$\Rightarrow 12k + 30 = 2430    \Rightarrow 12 k = 2400 \Rightarrow k = 200$
$\therefore$ C's share $= z = 5k + 15 = 5 \times 200 + 15 = Rs. 1015$

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 $7:4$