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

Which of the following is/are true regarding the ratio of the national flag?

  1. Ratio of the length of the height of the flag shall be 3:2

  2. The ratio of the length to the width of the flag shall be 3:2

  3. The ratio of the length to the height of the flag shall be 2:3

  4. Both a and b
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Indian national flag has an official ratio of 3:2 for length to width (or height). The Flag Code of India specifies this proportion. Option A and B both refer to the length:height/width ratio being 3:2, making D technically correct under the standard interpretation.

Multiple choice

Divide rupees 672 in the ratio 5:3

  1. 450:220

  2. 420:252

  3. 430:252

  4. 420:254
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total parts = 5 + 3 = 8. Value of one part = 672 / 8 = 84. First part = 5 * 84 = 420. Second part = 3 * 84 = 252.

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

The condition for two ratios to be equal is

  1. Product of means is equal to antecedents

  2. Product of extremes is equal to consequents

  3. Antecedents are equal to consequents

  4. Product of means is equal to product of extremes
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For the ratio to be equal the product of mean =product of extremes
for ex   $\dfrac{a}{b}=\dfrac{c}{d}$
product of $a\times d=b\times c$
where
$a\times d$ $=$product of extreme.
and$b\times c$ $=$ product of means.

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

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

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

$A\, :\, B\, = \, \displaystyle {\frac{1}{2}\, :\, \frac{3}{8}\,  =\, 4\, :\, 3,}$


$B\, :\, C\, = \, \displaystyle {\frac{1}{3}\, :\, \frac{5}{9}\, =\, 3\, :\, 5,}$
$C\, :\, D\, = \, \displaystyle {\frac{5}{6}\, :\, \frac{3}{4}\, =\, 10\, :\, 9,}$ 
$\Rightarrow A : B = 4 : 3, B : C = 3 : 5 \, and \, C : D = 5 : \displaystyle \frac{9}{2}$
$\Rightarrow A : B : C : D = 4 : 3 : 5 : \displaystyle \frac{9}{2}$
$= 8 : 6 : 10 : 9$

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

Two numbers are respectively 20% and 50% more than a third number The ratio of the two numbers is

  1. 2 : 5

  2. 3 : 5

  3. 4 : 5

  4. 6 : 7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the third number be x.
Then first number=120% of x=$\frac{120}{100}\times x=\frac{6x}{5}$
Second number=150% of x$\frac{150}{100}\times x=\frac{3x}{2}$
$\therefore$Ratio of first two number=$\frac{6x}{5}:\frac{3x}{2}=12x:15x=4:5$

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

Find the reduced form of the ratio of the first quantity to second quantity.
$3$ years $4$ months, $5$ years $8$ months.

  1. 17:10

  2. 10:17

  3. 10:15

  4. 15:10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

firstly year change into months

$1$ year = $12$ months 
$3$ years = 12x3 = $36$ months
$5$ years = 12x5 = $60$ months
Then reduced form are in ratio
\begin{array}{l} \frac { { 3\, years\, \, 4\, months } }{ { 5years\, \, 8\, \, months } }  \ =\frac { { \left( { 36+4 } \right) \, \, months } }{ { \left( { 60+8 } \right) \, \, months } }  \ =\frac { { 40 } }{ { 68 } }  \ =\frac { { 10 } }{ { 17 } } =10:17 \end{array}

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

Find the reduced form of the ratio of the first quantity to second quantity.
$7$ minutes $20$ seconds, $5$ minutes $6$ seconds.

  1. 111:345

  2. 234:151

  3. 220:153

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

Reduced form of 7 min 20 sec, 5 min 6 sec is 

firstly change minute in second 
\begin{array}{l} \frac { { 7\times 60+20 } }{ { 5\times 60+6 } }  \ =\frac { { 420+20 } }{ { 300+6 } }  \ =\frac { { 440 } }{ { 306 } }  \ =\frac { { 220 } }{ { 153 } } =220:153 \end{array}