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

A sum of $Rs.350$ is to be divided between $A$ and $B$ in the ratio $3:4.$ If the amount distributed in the ratio $4:3$ the amount gained by $A$ is 

  1. $Rs.10$
  2. $Rs.30$
  3. $Rs.50$
  4. $Rs.100$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let $A$ got $3x$ and $B$ got $4x$. Then,

$3x+4x=350$

$7x=350$

$x=50$

Therefore, $A$ got $150 Rs.$ and $B$ got  $200 Rs.$.

If the ratio was $4 : 3,$ $A$ got $Rs. 200$ and $B$ got $Rs. 150$.

Therefore, the amount gained by $A = Rs. 50$

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

Instead of dividing $Rs.\,117$ among $P,Q,R$ in the ratio $\displaystyle\frac{1}{2}\colon\displaystyle\frac{1}{3}\colon\displaystyle\frac{1}{4}$, by mistake it was divided in the ratio $2\,\colon\,3\,\colon\,4$. Who gained in the transaction? 

  1. only $P$
  2. only $Q$
  3. only $R$
  4. both $Q$ and $R$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Desired ratio $=\displaystyle\frac{1}{2}\colon\displaystyle\frac{1}{3}\colon\displaystyle\frac{1}{4}=\displaystyle\frac{1}{2}\times12\colon\displaystyle\frac{1}{3}\times12\colon\displaystyle\frac{1}{4}\times12$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=6\colon4\colon3$
Ratio by mistake $=2\colon3\colon4=6\colon9\colon12$
Hence, it is clear that both $Q$ and $R$ gained in the transaction.

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

If Rs. $60$ is divided into two parts in the ratio $2 : 3,$ then the difference between those two parts is ______

  1. Rs. $10$
  2. Rs. $12$
  3. Rs. $5$

  4. none
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rs. $60$ is divided into two parts $2:3$.
Their sum is $2+3=5$.
Thus first part is $60\, \times\, \displaystyle \frac {2}{5} =$ Rs. $24$
and second part will be $60\, \times\, \displaystyle \frac {3}{5}\, =$ Rs. $36$.
Therefore, difference will be $ 36 - 24 =$ Rs. $12$.

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

A number $351$ is divided into two parts in the ratio $2 : 7.$ Find the product of the numbers.

  1. $20,294$
  2. $21,294$
  3. $25,295$
  4. $31,294$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the numbers be $2x$ and $7x$.
$2x + 7x = 351$
$x = 39$
Therefore, product of the numbers is $2x \times 7x$ $=$ $14x^2$
$=$ $14\, \times\, (39)^2$
$= 21,294$

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

The ratio of the heights of A and B is $4 : 3$ . If B is $1.2$m tall then the height of A is:

  1. $0.9$ m
  2. $1.8$ m
  3. $1.6$ m

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Height of A $\displaystyle =\frac{4}{3}\times$ height of B
                    

                    $\displaystyle =\dfrac{4}{3} \times 1.2 = 1.6$ m

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

If Rs. $2,600$ is divided among three persons $A, B$ and $C$ in the ratio $\dfrac {1}{2} : \dfrac {1}{3} : \dfrac {1}{4}$, how much does $A$ get?

  1. Rs. $ 600$
  2. Rs. $ 800$
  3. Rs. $ 1.000$
  4. Rs. $ 1,200$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Among three persons Rs. $2600$ is divided in the ratio as $\dfrac {1}{2}, \dfrac {1}{3}, \dfrac {1}{4}$.
LCM of $\dfrac {1}{2} : \dfrac {1}{3} : \dfrac {1}{4} $ is $ 6 : 4 : 3$.
Therefore, $A$'s share $= \dfrac {6}{13} \times  2,600 =$ Rs. $1,200$.

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 $3 : 2 : 5$ and the sum of their squares is $1862$. What are the three numbers?

  1. $18, 12, 30$
  2. $24, 16, 40$
  3. $15, 10, 25$
  4. $21, 14, 35$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the three numbers b $3x, 2x, 5x$

Sum of their squares is $1862$.
Therefore, $(3x)^{2} + (2x)^{2} + (5x)^{2} = 1862$
$\Rightarrow 38x^{2} = 1862$
$\Rightarrow  x^{2} = 1862 \div 38 = 49$
$\Rightarrow x = 7$ 
The numbers are $21, 14, 35$.

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

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

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, $\displaystyle x + \frac{9x}{4} + 4x = 116$
$\Rightarrow 4x + 9x + 16x = 116 \times 4$
$\Rightarrow 29 x = 116 \times 4 \Rightarrow x = \displaystyle \frac{116 \times 4}{29} = 16$
$\therefore \text{2nd number}= \displaystyle \frac{9}{16} \times 4 \times 16 = 36$