Quantitative Aptitude

Fractions and Percentages

344 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.

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Fractions and Percentages Questions

Multiple choice maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

If $40$%of a number is equal to two-third of another number, what is the ratio of first number to the second numbers?

  1. 2:5

  2. 3:7

  3. 5:3

  4. 7:3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$(l-m) (lm+l+x^{2})=0$
 Let the number be $x _{1} y$
Given :- $40\% $ of $(x) = \dfrac{2}{3}$ of $(y)$
to find :-$\dfrac{x}{y}= ?$
$\dfrac{40}{100} \times x = \dfrac{2}{3} \times y$
$\dfrac{x}{y}= \dfrac{2}{3} \times \dfrac{100}{40}$
$\Rightarrow \dfrac{x}{y}= \dfrac{5}{3}$
Multiple choice maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

If the numerator of a fraction is increased by $300\%$ and the denominator is increased by $500\%$, the resultant fraction is $\displaystyle\frac{5}{12}$. What was the original fraction?

  1. $\;\displaystyle\frac{8}{5}$
  2. $\;\displaystyle\frac{5}{8}$
  3. $\;\displaystyle\frac{12}{5}$
  4. $\;\displaystyle\frac{5}{7}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the original fraction be $\dfrac {p}{q}$. 

Then, $\displaystyle\frac{p+\displaystyle\frac{300}{100}P}{q+\displaystyle\frac{500}{100}P}=\displaystyle\frac{5}{12}$
$\Rightarrow \displaystyle\frac{4p}{6q}=\displaystyle\frac{5}{12}$
$\Rightarrow\;\displaystyle\frac{p}{q}=\displaystyle\frac{5}{12}\times\displaystyle\frac{6}{4}=\displaystyle\frac{5}{8}$

Multiple choice maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

If $m > 0$ and $x$ is $m$ percent of $y$, then in terms of $m$, $y$ is what percent of $x$ ? 

  1. $100$ m
  2. $\dfrac{1}{100}$ m
  3. $1$ m
  4. $10$ m
  5. $\dfrac {10000}{m}$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Given that : x is $m\%$ of y

$\Rightarrow x = \cfrac{m}{100} \times y$ 
Now, let's say that y is $k\%$ of x, then
$y = \dfrac{k}{100} \times x$
But $x= \cfrac{m}{100} \times y$
$\therefore y =\cfrac{k}{100} \times \cfrac{m}{100} \times y$
$k = \cfrac{10000}{m}$

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

Sunny was given $\displaystyle \frac{1}{3}$ of a sum of money and Ankur was given $\displaystyle \frac{1}{3}$ of what was left. What is Ankur's share as a fraction of Sunny's Share?

  1. $\displaystyle \frac{2}{9}$
  2. $\displaystyle \frac{1}{3}$
  3. $\displaystyle \frac{2}{3}$
  4. $\displaystyle \frac{1}{9}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Sunny gives $\dfrac { 1 }{ 3 }$ of his money
Left amount will be $ 1-\dfrac { 1 }{ 3 } = \dfrac { 2 }{ 3 }$ 
Amount received by Ankur is $\dfrac { 1 }{ 3 }$ of left amount $(\frac { 2 }{ 3 }$  of total amount $)$ 
Amount received by Ankur will be $\dfrac { 1 }{ 3 } \times \dfrac { 2 }{ 3 }$ of total amount $= \dfrac { 2 }{ 9 }$ of total amount
Ankur's share as a fraction of Sunny's share is $\dfrac{\frac{2}{9}}{\frac{1}{3}}=\dfrac{2}{3}$
So Correct answer will be option C
Multiple choice maths part number dividing fractions division of a fractions division of a fraction

$\dfrac{25 \% \, of  \ 50\% \ of \ 100 \%}{25 \,of \,100 \times 50 \%\, of \,100 }$ is equal to ______ .

  1. $ 0.0001\%$
  2. $ 0.1\%$
  3. $ 0.01\%$
  4. $ 1\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given $\cfrac {25\%\quad of\quad 50\%\quad of\quad 100\%}{25\quad of\quad 100\times 50\%\quad of\quad 100}$

So, first solving solving numerator
$\cfrac {25}{100}$ of $\cfrac {50}{100}$ of $\cfrac {100}{100}$ 
$\implies \cfrac {25}{100}\left(\cfrac {50}{100}\left(\cfrac {100}{100}\right)\right)\quad equation (1)$  
Now taking denominator
$25$ of $100\times 50\%$ of $100$ 
So, $25$ of $100$ means $\cfrac {25}{100}$ which is $\cfrac {1}{4}$
$50\%$ of $100=\cfrac {50}{100}\times 100=50$
So, denominator becomes $\cfrac {1}{4}\times 50\quad equation (2)$
$\cfrac {Numerator}{Denominator}=\cfrac {equation (1)}{equation (2)}$
$=\cfrac {\cfrac {25}{100}\left(\cfrac{50}{100}\left(\cfrac{100}{100}\right)\right)}{\cfrac {1}{4}\times 50}$
$=\cfrac {\cfrac {1}{4}\times \cfrac {1}{2}}{\cfrac {1}{4}\times 50}$
$=\cfrac {1}{2}\times 50$
In terms of percent $=\cfrac {1}{100}\times 100=1\%$

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

The least number among $\displaystyle \frac{4}{9}, \, \sqrt{\frac{9}{49}},$ 0.45 and $(0.8)^2$ is

  1. $\displaystyle \frac{4}{9}$
  2. $\displaystyle \sqrt{\frac{9}{49}}$

  3. 0.45
  4. $(0.8)^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
: Decimal equivalents of the given numbers.
$\displaystyle \frac{4}{9} \, = \, 0.44; \, \sqrt{\frac{9}{49}} \, = \, \frac{3}{7} \, = \, 0.43$
$\displaystyle 0.45 \, and \, (0.8)^2 \, = \, 0.64$
$\displaystyle \therefore$ Least number is 0.43
$\displaystyle = \, \sqrt{\frac{9}{49}}$
Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

When a number is reduced by $4$, it becomes $80\%$ of itself. Find the number.

  1. $20$
  2. $30$
  3. $40$
  4. $50$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let the Number be $X$
Number is reduced by $4$ i.e. $X-4$.
Now number becomes $80 \% $ of itself
$X-4 =  80\%  $ of $X$
$ \Rightarrow X-4 = \dfrac{80}{100}\times X$
$ \Rightarrow X-4 = 0.8 X$
$ \Rightarrow 0.2X=4 $
$ \Rightarrow X=20 $
The number is $20$.