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 mixture types of ratios ratios in proportion mathematical logic

Increasing Rs $40$ in the ratio $5 : 4$ we get?

  1. $10$
  2. $60$
  3. $50$
  4. $80$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Increasing Rs $40$ in the ratio $5.4$ implies that the ratio of the new quantity to the old quantity is $5 : 4$.
$\therefore$ Let the increased quantity be x
$\therefore \dfrac {\text {New amount}}{\text {original amount}} = \dfrac {x}{40} = \dfrac {5}{4}$
$\therefore x = 50$
that is the increased quantity is $50$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

Two numbers are in the ratio of $1:2$. If $7$ be added to both, their ratio changes to $3:5$. The greater number is.

  1. $20$
  2. $24$
  3. $28$
  4. $32$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the numbers are $x$ and $y$ whose ratio is $1 : 2$

$\dfrac{x}{y}=\dfrac{1}{2}$
$\Rightarrow 2x=y$.......................................(1)
Given that when 7 added to both numbers, ratio changes to $3 : 5$
$\dfrac{x+7}{y+7}=\dfrac{3}{5}$
$\Rightarrow 5(x+7)=3(y+7)$
$\Rightarrow 5x+35=3y+21$
$\Rightarrow 5x-3y=21-35$
$\Rightarrow 5x-3y=-14$.................(2)
Put the value of $y=2x$ as per (1) we get
$5x-3(2x)=-14$
$5x-6x=-14$
$x=14$
Put the value of $x=14$ in (1) we get
$2\times 14=y$
$\Rightarrow y=28$
Then numbers are$ 14 ,28$
Then greater number is $28$.

Multiple choice botany classical genetics incomplete dominance deviation from mendelism inheritance

In incomplete dominance, ratio of red: pink: white is

  1. 1:2:1

  2. 1:1:2

  3. 1:2:2

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

Incomplete Dominance is the blending of alleles to create a phenotype that is a combination of both traits the alleles code for. Incomplete dominance is a type of non-Mendelian genetics.

For instance, snapdragon flowers can be either red, white, or pink. If they followed Mendel's inheritance patterns of simple dominance, the flowers would either be red or white in a 3:1 ratio. However, with snapdragon flowers, the ratio of red to pink to white is 1:2:1. This was Mendel's genotype ratio of homozygous dominant to heterozygous to homozygous recessive. This means that the heterozygous plant was actually blending the "dominant" and "recessive" alleles instead of the dominant trait completely masking the recessive trait in the phenotype of the plant. Thus, the correct answer is option A.

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

 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 $

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

By mistake instead of dividing Rs. $117$ among $A,B$ and $C$ into the ratio $\displaystyle \frac{1}{2}: \frac{1}{3}: \frac{1}{4}$ , it was divided in the ratio of $2:3:4$ . Who gains the most and by how much?

  1. $A, Rs. 28$
  2. $B, Rs. 3$
  3. $C, Rs. 20$
  4. $C, Rs. 25$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To convert $\displaystyle \frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ into normal ratio, multiply each fraction by the LCM$(2,3,4) = 12$

$\displaystyle= 12\times \frac{1}{2}:12\times\frac{1}{3}:12\times\frac{1}{4}$
= $\displaystyle 6:4:3 $
Thus, A would have got $\displaystyle \frac{6}{6+4+3} \times 117 = 54$

B would have got $\displaystyle \frac{4}{6+4+3} \times 117 = 36$

And C would have got $\displaystyle \frac{3}{6+4+3} \times 117 = 27$

Instead Rs. $117$ have been divided in the ratio of $2:3:4$

A gets $\displaystyle \frac {2}{2+3+4} \times 117 = 26$

B gets $\displaystyle \frac {3}{2+3+4} \times 117 = 39$

C gets $\displaystyle \frac {4}{2+3+4} \times 117 = 52$

Thus, by changing the ratio,
A gained $26 - 54$ = -$28$
B gained $39 - 36$ = $3$
And C gained $52 - 27 = 25$
Thus, C's gain of $25$ is the most.