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 mixture types of ratios ratios in proportion mathematical logic

$A, B$ and $C$ enter into partnership by making investments in the ratio $3:5:7$. After a year, $C $ invests another Rs. $337600$ while $A$ withdraws Rs. $45600$. The ratio of investments then changes to $24:59:167$. How much did $A$ invest initially?

  1. Rs. $45600$
  2. Rs. $96000$
  3. Rs. $141600$

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

Let initial investments by $A, B$ and $C$ are $3x, 5x, 7x$

After a year:
$A$'s investment $=3x-45600$
$C$'s investment $=7x +337600$
$(3x-45600):5x : (7x+337600) = 24 : 59 : 167$
Solving this we will get $x=47200$
So, A's initial investment was $=3x = 3\times47200 = 141600$

Multiple choice maths part number dividing fractions division of a fractions division of a fraction

If $Rs.510$ be divided among $A,B,C$ in such a way that $A$ gets $\dfrac{2}{3}$ of what $B$ gets and $B$ gets $\dfrac{1}{4}$ of what $C$ gets, then their shares are respectively:

  1. $Rs.120, Rs.240, Rs.150$
  2. $Rs.60, Rs.90, Rs.360$
  3. $Rs.150, Rs.300, Rs.60$
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$A=\dfrac{2}{3}B$

$B=\dfrac{1}{4}C$

$\Rightarrow C=4B$

$A+B+C=510$                                            

$=2B/3+B+4B=510$
                               
$=2B+3B+12B=510\times 3$                      

$=17B=510\times 3$ 
                                             
$B=30\times 3=90$

$A=\dfrac{2\times 90}{3}$

$=60$

 $C=4\times 90$

$=360$.

Multiple choice business mathematics and statistics introduction to index number introduction to index numbers index numbers applied statistics

Index numbers are expressed in:

  1. Ratios

  2. Squares

  3. Percentages

  4. Combinations
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\Rightarrow$  Index numbers are expressed in : $Percentage$.

$\Rightarrow$  Index numbers are expressed in terms of percentages to show the extent of relative change.
$\Rightarrow$  Index numbers measure relative changes. They measure the relative change in the value of a variable or a group of related variables over a period of time or between places.
$\Rightarrow$  Index numbers measures changes which are not directly measurable.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

Two numbers are in the ratio $3 : 5$. If $9$ is subtracted from each, the new numbers are in the ratio $12 : 23$. Find the smaller number.

  1. $27$
  2. $33$
  3. $49$
  4. $55$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the numbers be $x$ and $y$

$\dfrac{x}{y}=\dfrac{3}{5}$ ...(1)

According to the question,

$\dfrac{x-9}{y-9}=\dfrac{12}{23}$ ...(2)

$x=\dfrac{3y}{5}$

$ \dfrac { \dfrac { 3y }{ 5 } -9 }{ y-9 } =\dfrac { 12 }{ 23 }  $

$  \dfrac { 3y-45 }{ 5y-45 } =\dfrac { 12 }{ 23 } $

$23(3y-45)=12(5y-45)$

$69y-1035=60y-540$

$9y=1035-540=495$

$y=55$

From (1)

$\dfrac{x}{55}=\dfrac{3}{5}$

Thus the smaller number is 33

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

A fruit salad is made from pineapples, pears, and peaches mixed in the ratio of $2$ to $3$ to $5$, respectively, by weight. What fraction of the mixture by weight is pineapple?

  1. $\dfrac{1}{5}$
  2. $\dfrac{3}{10}$
  3. $\dfrac{2}{5}$
  4. $\dfrac{1}{2}$
  5. $\dfrac{2}{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given,
A fruit salad is made from pineapples,pears and peaches mixed in the ratio $2:3:5$ respectively by weight
total weight of mixture as per ratio is $\left( 2+3+5 \right) =10$
Fraction of weight in  mixture  pineapple will be $\dfrac { 2 }{ 10 } =\dfrac { 1 }{ 5 } $
Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

Mark the correct alternative of the following.
If A, B, C divide Rs. $1200$ in the ratio $2 : 3 : 5$, then B's share is?

  1. Rs. $240$
  2. Rs. $600$
  3. Rs. $380$
  4. Rs. $360$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since they divide Rs. $1200$ in the ratio $2:3:5$ then let shares of them will be $2x,3x$ and $5x$.

Then according to the problem we get,
$2x+3x+5x=1200$
or, $x=120$.
So share of B is Rs. $120\times 3=360$.

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

 The third proportion between : $2$ and $8$

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

If a : b :: b : c, then we say that a, b, c are in continued proportion, and c is the third proportional of a and b.

Here, $ {b}^{2} = ac $ or $ b = \sqrt {ac} $

So, for $ 2, 8 $, the third proportional is $ b = \sqrt {ac} = \sqrt {2 \times 8} = \sqrt {16} = 4 $