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 percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

If p is 6 times that of q, what percent is q less than p?

  1. $12\, \displaystyle \frac{1}{2}\, \%$
  2. $83\, \displaystyle \frac{1}{3}\, \%$
  3. $6\, \displaystyle \frac{1}{4}\, \%$
  4. $33\, \displaystyle \frac{1}{3}\, \%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$p = 6q$
$p - q = 6q - q = 5q$
$\therefore$ q is less than p by $\displaystyle \frac{p\, -\, q}{p}\, \times\, 100\, \%$
$=\, \displaystyle \frac{5q}{6q}\, \times\, 100\, \%$ $=\, 83\, \displaystyle \frac{1}{3}\, \%$

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

If 'a' is  x % more than 'b' and 'b' is y % less than 'a'. then the relation between x and y is

  1. $\displaystyle \frac{1}{x}\, +\, \displaystyle \frac{1}{y}\, =\, \displaystyle \frac{1}{100}$
  2. $\displaystyle \frac{1}{y}\, -\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{1}{100}$
  3. $\displaystyle \frac{1}{x}\, -\, \displaystyle \frac{1}{y}\, =\, 100$
  4. $\displaystyle \frac{1}{y}\, -\, \displaystyle \frac{1}{x}\, =\, 100$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$y\, \%\, =\, \displaystyle \frac{100\, \times\, x}{100\, +\, x} \%$


$\Rightarrow y\, =\, \displaystyle \frac{100\, \times\, x}{100\, +\, x}$

$\Rightarrow \displaystyle \frac{1}{y}\, =\, \displaystyle \frac{100\, +\, x}{100\, \times\, x}\, =\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{1}{100}$

$\Rightarrow \displaystyle \frac{1}{y}\, -\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{1}{100}$

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

The % of total quantity represented by a $60^{circ}$ sector in a pie diagram is 

  1. $6 \displaystyle \frac{1}{4}$ %
  2. $16\, \displaystyle \frac{2}{3}$ %
  3. $11\, \displaystyle \frac{1}{9}$ %

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

$\displaystyle \frac{x}{100}\, \times\, 360\, =\, 60^{\circ}$


$x\, =\, 60\, \times\, \displaystyle \frac{100}{360}\, =\, \displaystyle \frac{100}{6}\, =\, 16\, \displaystyle \frac{2}{3}$ %

Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

A number x is decreased by m% and some other number y is increased by m%. If both the results are equal, find m in terms of x and y. Also, find m if $\displaystyle 2x=3y$.


  1. $\displaystyle m=\frac{100\left ( x+y \right )}{x+y};m=10$
  2. $\displaystyle m=\frac{100\left ( x-y \right )}{x-y};m=20$
  3. $\displaystyle m=\frac{100\left ( x+y \right )}{x+y};m=30$
  4. $\displaystyle m=\frac{100\left ( x-y \right )}{x+y};m=20$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given $ \frac {100 - m}{100} \times x = \frac {100 + m}{100} \times y $
$ => 100x - mx = 100y + my $
$ => 100x - 100y = mx + my $
$ => 100 (x-y) = m (x + y) $
$ => m = \frac {100(x-y)}{x+y} $

When , $ 2x = 3y => x = \frac {3y}{2} $
We have, $ m = \frac {100(\frac {3y}{2} -y)}{\frac {3y}{2} +y} $
$ => m =\frac {100(\frac {y}{2})}{\frac {5y}{2}} $
$ => m =\frac {100}{5} = 20 $

Multiple choice evs water in our life where do we get water from? why conserve water uses of water

Percentage of total water found as fresh water is 

  1. 46%

  2. 32%

  3. 16%

  4. 2.5%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Only 2.5% of total water present on the surface of the earth is present as freshwater which can be used for drinking and is potable. Rest of it is present in the form of seawater which is not salt-free and cannot be used for drinking. So, freshwater should be used very judiciously and used for drinking.

So, option D is the correct answer.

Multiple choice maths measuring time time in 24 hour clock time difference time

What percent of $1$ day is $36$ minutes?

  1. $25\%$
  2. $2.5\%$
  3. $3.6\%$
  4. $0.25\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Total hours in 1 day $=  24$ hrs
$1$ hour $= 60$ minutes
Total minutes in $1$ day $=  24 \times 60 = 1440$ minutes
Percent of $36$ min in $1$ Day is 
$= \dfrac{36}{1440} \times 100  \% = 2.5 \%$
Multiple choice maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

A student was asked to simplify $\displaystyle \frac{0.6\times 0.6\times 0.6+0.5\times 0.5\times 0.5+0.1\times 0.1-0.09}{0.6\times 0.6+0.5\times 0.5+0.1\times 0.1-0.41}$ and his answer was 0.6 By what per cent was his answer wrong

  1. 25%

  2. 100%

  3. 50%

  4. 120%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle \frac{0.6\times 0.6\times 0.6+0.5\times 0.5\times

0.5+0.1\times 0.1-0.09}{0.6\times 0.6+0.5\times 0.5+0.1\times

0.1-0.41}$


$\dfrac{0.216+0.125+0.01-0.09}{0.36+0.25+0.01-0.41}= \dfrac{0.261}{0.21} = 1.2$

Student got answer as $0.6$

Hence His Answer was wrong with $\dfrac{0.6}{1.2}\times 100= 50$%

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

Two-third of one-seventh of a number is $87.5$% of $240$. What is the number?

  1. $2670$
  2. $2450$
  3. $2205$
  4. $1470$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\dfrac {2}{3}$ of $\dfrac {1}{7}$ of a number say $x$ is $87.5\%$ of $240$.

$\therefore \displaystyle \frac{2}{3}\times\frac{1}{7}\times x=\frac{87.5}{100}\times240$

$\displaystyle \Rightarrow x =\frac{87.5\times240\times3\times7}{2\times100}=2205$
therefore, the number is $2205$.