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 ratio, proportion and unitary method converting to ratios finding ratios other quantities

If $A : B = \displaystyle \frac{1}{2} : \dfrac {3} {8},   B : C = \frac{1}{3} : \frac{5}{9} $ and $\displaystyle C : D = \frac{5}{6} : \frac{3}{4}$, then the ratio $A : B : C : D$ is

  1. $6 : 4 : 8 : 10$
  2. $6 : 8 : 9 : 10$
  3. $8 : 6 : 10 : 9$
  4. $4 : 6 : 9 : 10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$A:B = \displaystyle \frac{1}{2} : \frac{3}{8} = \frac{1}{2} \div \frac{3}{8} = \frac{1}{2} \times \frac{8}{3} = \frac{4}{3} = 4 : 3 = 8:6$


$B:C = \displaystyle \frac{1}{3} : \frac{5}{9} = \frac{1}{3} \div \frac{5}{9} = \frac{1}{3} \times \frac{9}{5} = \frac{3}{5} = 3 : 5 = 6 : 10$

$C:D = \displaystyle \frac{5}{6} : \frac{3}{4} = \frac{5}{6} \div \frac{3}{4} = \frac{5}{6} \times \frac{4}{3} = \frac{10}{9}  = 10 : 9$

$\therefore A : B : C : D = 8 : 6 : 10 : 9.$

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

The ratio of $A$ to $B$ is $4 : 5$ and that of $B$ to $C$ is $2 : 3.$ If $A$ equals $800,$ then $C$ equals

  1. $1000$
  2. $1200$
  3. $1500$
  4. $2000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle \frac{A}{B} = \frac{4}{5} $ and $\displaystyle \frac{B}{C} = \frac{2}{3}$
To make both the values of B equal, take LCM of both values of B, i.e., 5 and 2 which is equal to 10.
$\therefore \displaystyle \frac{A}{B} = \frac{4}{5} = \frac{8}{10}$ and $\displaystyle \frac{B}{C} = \frac{2}{3} = \frac{10}{15}$
$\Rightarrow A : B : C =8 : 10 : 15$
$\Rightarrow A = 8x, B = 10 x, C = 15 x$
Given, $A = 800 \Rightarrow 8x = 800$
$\Rightarrow x = 100       \Rightarrow C = 1500$

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

If $x : y = 3 : 1$ then find the ratio $\displaystyle x^{3}-y^{3}:x^{3}+y^{3}$

  1. $13 : 14$
  2. $12 : 13$
  3. $11: 14$
  4. $10 : 13$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let $x = 3k$ and $y = k$
Then $\displaystyle \frac{x^{3}-y^{3}}{x^{3}+y^{3}}$


$=\dfrac{(3k)^{3}-k^{3}}{(3k)^{3}+k^{3}}$


$=\dfrac{27k^{3}-k^{3}}{27k^{3}+k^{3}}$

$=\dfrac{26k^{3}}{28k^{3}}$

$=\dfrac{13}{14}$

$=13:14$

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

In an office the working hours are 9:30 AM to 4:30 PM and in between 20 minutes are spent on lunch Find the ratio of office hours to the time spent for lunch-

  1. $21:1$
  2. $1:14$
  3. $7:30$
  4. $30:7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total time in office $ = 9:30  to  4:30  = 7  hours  $

Ratio of two quantities can be found when they are of same units.

So, $ 7  hours   = 7 \times 60 = 420  minutes   $
Hence, ratio $ = \dfrac {420  min }{20  min } = 21:1 $

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

The continued ratio of $4 : 3$ and $5 : 6$ is ____

  1. $4 : 15 : 6$
  2. $4 : 5 : 6$
  3. $20 : 15 : 12$
  4. $20 : 15 : 18$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$Ratio 1 = 4 : 3$
$Ratio 2 = 5 : 6$
Multiplying ratio $1$ by antecedent of ratio $2$ and ratio $2$ by consequent of ratio $1$,
Ratio $1 = 20 : 15$
Ratio $2 = 15 : 18$
Thus, for two ratios $a : b$ and $b : c, a : b : c$ is called the continued ratio.
$\therefore 20 : 15 : 18$ is the continued ratio for $4 : 3$ and $5 : 6$.

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

The continued ratio of $2 : 5$ and $6 : 7$ is _____

  1. $2 : 5 : 7$
  2. $2 : 5 : 6$
  3. $12 : 30 : 35$
  4. $12 : 10 : 42$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$R _{1}$ = $2 : 5$
$R _{2}$ =$ 6 : 7$
Multiplying the LCM of the consequent of ratio $1$ and antecedent of ratio $2$, to both the ratios.
$R _1$ = $12 : 30$
$R _2$ = $30 : 35$
Thus, the continued ration for $2 : 5$ and $6 : 7$ is $12 : 30 : 35$

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

In a box, the ratio of the number of red marbles to that of blue marbles is $4 : 7$. which of the following could be the total number of in the box?

  1. $14$
  2. $21$
  3. $22$
  4. $28$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$With\quad ratios,add\quad all\quad the\quad parts\quad together\quad to\quad get\quad a\quad total.In\quad this\quad case,it\quad is\quad 4red\quad and\quad 7blue.$


$7+4=11.$

$Therefore,the\quad lowest\quad total\quad number\quad of\quad marbles\quad is11.The\quad answer\quad will\quad be\quad any\quad number\quad divisible\quad by\quad 11.$

$Hence\quad it\quad is\quad 22.$

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

The ratio of $\left(\displaystyle\dfrac{1}{3}\text{ of Rs. }9.30\right)$ to $(0.6\text{ of Rs. }1.55)$ is ___________.

  1. $1:3$
  2. $10:3$
  3. $3:10$
  4. $3:1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle\frac{1}{3}$ of Rs. $9.30=Rs. \left(\displaystyle\frac{1}{3}\times 9.30\right)=Rs. 3.10$
$0.6$ of Rs. $1.55=$Rs. $(0.6\times 1.55)=$ Rs. $0.93$
$\therefore$ Required ratio$=3.10:0.93=10:3$.

Multiple choice

The ratio of 5m to 10km is

  1. 2000 : 1

  2. 1 : 2000

  3. 1 : 2

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

Convert units to be the same: 10 km = 10,000 m. The ratio is 5 : 10,000. Dividing both by 5 gives 1 : 2000.