Quantitative Aptitude

Fractions and Percentages

307 Questions

Fractions and percentages form the foundation of quantitative aptitude, requiring the conversion of values between different formats. Questions cover percentage increases, fractional equivalents, and basic arithmetic manipulations. These concepts are heavily tested in SSC, banking, and railway competitive exams.

percentage calculationsfraction conversionspercentage increase problemsnumerator denominator changessuccessive percentages

Fractions and Percentages Questions

Multiple choice

Which fraction is greater than 1/2?

  1. 2/5

  2. 5/9

  3. 6/12

  4. 43/100
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To be greater than 1/2, the numerator must be more than half of the denominator. Since 5/9 is greater than 4.5/9, it is greater than 1/2.

Multiple choice

Which fraction is less than 1/2?

  1. 4/7

  2. 5/8

  3. 6/11

  4. 7/16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A fraction is less than 1/2 if the numerator is less than half of the denominator. For 7/16, half of 16 is 8, and 7 is less than 8.

Multiple choice

Which fraction is equal to one-half?

  1. 2/12

  2. 7/14

  3. 3/9

  4. 11/21
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A fraction is equal to 1/2 if the denominator is exactly twice the numerator. In 7/14, 14 is 2 times 7.

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

In expressing a length $81.472 \ km$ as nearly as possible with three significant digits, the percent error is

  1. $0.34\%$
  2. $0.034\%$
  3. $0.0034\%$
  4. $0.0038\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$81.472 km = 81472$ meters $= 81500$ meters with three significant digits.
$\displaystyle \therefore Error\%=\frac{81500-81472}{81472}\times 100=0.034\%$

Multiple choice chemistry the language of chemistry percent composition percentage composition and empirical formula empirical formula, percentage composition and molecular formula water of crystallisation

Determine the percentage composition of $K$ in $KMnO _4$.

  1. $31\%$
  2. $43.58\%$
  3. $25\%$
  4. $55\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
To find:- $\%$ composition of K in $KMnO _4$
A/c
Molar mass of $K=39$g
Molar mass of $KMnO _4=158$gm
$\%$ of k in $KMnO _4=\dfrac{39}{158}\times 100=24.68\%$
$\approx 25\%$.
Option C is correct.
Multiple choice maths perimeter, area and volume volume of prism and pyramid surface areas and volumes of solids recall the surface areas and volumes of different solid shapes

Each side of the base of a square pyramid is reduced by $20%$. By what percent must the height be increased so that the volume of the new pyramid is the same as the volume of the original pyramid?

  1. 20

  2. 40

  3. 46.875

  4. 56.25

  5. 71.875
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let $a$ be the side of the square.
Length of side of square when reduced by $20\% = a-\dfrac{20a}{100}=0.8a$
Let $a _1=0.8a$
Volume of pyramid $V=\dfrac { 1 }{ 3 } \times $ Area of base $\times height=\dfrac{1}{3}A\times h$
Area of base with side $a = { a }^{ 2 }$ 
${ a }^{ 2 }=0.8a$

${V} _{ 1 }=\dfrac { 1 }{ 3 } \times { \left( { a } _{1} \right)  }^{ 2 }\times { h } _{ 1 }$ 
${V} _{ 1 }=V$ ....... [Given]

$\Rightarrow \dfrac { 1 }{ 3 } { a }^{ 2 }\times h=\dfrac { 1 }{ 3 } { \left( 0.8 \right)  }^{ 2 }{ a }^{ 2 }\times { h } _{ 1 }$

$\therefore { h } _{ 1 }=1.5625h$ 

$\implies \dfrac { { h } _{ 1 }-h }{ h } =1.5625-1=56.25%$

$\therefore$  'h' need to be increase by $56.25$ 
Multiple choice chemistry introduction to analytical chemistry interpreting a balanced chemical reaction percentage yield stoichiometric calculations

How is percent yield calculated?

  1. $\displaystyle \text { Percent yield } = \dfrac { \text { actual yield } }{ \text { theoretical yield } } \times 100 $
  2. $\displaystyle \text { Percent yield } = \dfrac { \text { actual yield } }{ \text { theoretical yield } \times 100 } $
  3. $\displaystyle \text { Percent yield } = \dfrac { \text { actual yield } }{ \text { theoretical yield } } $
  4. $\displaystyle \text { Percent yield } = \dfrac { \text { theoretical yield } }{ \text { actual yield } } $
  5. $\displaystyle \text { Percent yield } = \text { actual yield } \times \text { theoretical yield } \times 100 $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle   \text { Percent yield } = \dfrac { \text { Actual yield } }{ \text { Theoretical yield } } \times  100 $ %

For example,
If actual yield is 10 g and theoretical yield is 20 g, 


Then, percent yield will be-$\displaystyle  \dfrac {10 g}{20g}  \times 100 = 50$ %.


Hence, option $A$ is correct.