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 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 $2205$.

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

$0.15 \% \text { of } 33 \frac { 1 } { 3 } \% \text { of } \mathrm { Rs } .10,000$ is?

  1. $\mathrm { Rs } .0 .05$
  2. $\mathrm { Rs } .5$
  3. $\mathrm { Rs } .105$
  4. $\mathrm { Rs } .150$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given 


$0.15\% \times 33\dfrac 13\% \times 10000$

$\implies \dfrac {15}{100}\times \dfrac 1{100}\times \dfrac {100}3 \times \dfrac 1{100}\times 10000$

$\implies \dfrac {15}3=5$

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

What is the percentage approximate for the fraction $\dfrac{12}{35}$?

  1. $34.28\%$
  2. $23.78\%$
  3. $30.12\%$
  4. $29.10\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To get the percent you will divide the numerator by the denominator.

Then multiply $100$ to the answer and add the percent sign.
therefore, the percentage approximate value if $\dfrac{12}{35}\times 100 = 34.28$ $\%$.

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

Which of the following statement/formulae is correct for Percentage Error?

  1. $\cfrac { \left| Approx.value-Exact\quad value \right| }{ Exact\quad value } $
  2. $\cfrac { \left| Exact\quad value-Approx.value \right| }{ Exact\quad value } $
  3. $\cfrac { \left| Approx.value-Exact\quad value \right| }{ Approx.value } \quad $

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

The approximate values is the estimated values and the exact value is the real value.

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

Sam does an experiment to find how long it takes an apple to drop $2$ meters. Sam measures $0.62$ seconds, which is an approximate value. Calculate the error percentage.

  1. $4\%$
  2. $3\%$
  3. $6\%$

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

we know that ,
$s=\dfrac{at^2}{2}$
$a=g=9.81 msec^{-2}$
$2=\dfrac{9.81t^2}{2}$
$t=\sqrt{\dfrac{4}{9.81}}$
$t=0.6385$
Therefore, error is $(0.6385-0.62)\times 100%=3%$
$3%$ is the error percentage.

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

They forecast 20 mm of rain, but we really got 25 mm. Find the error in percentage.

  1. $-20\%$
  2. $-10\%$
  3. $10\%$

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

$\dfrac{Approximate Value - Exact Value}{Exact \  Value} \times100$
$\dfrac{20-25}{25} \times 100$ = $\dfrac{-5}{25} \times 100$
$\dfrac{-100}{5}$ = $-20$
Percentage of error $ = - 20\%$.

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

Two numbers are less than a third number by $30\%$ and $37\%$ respectively. How much percent is the second number less than the first?

  1. $10\%$
  2. $15\%$
  3. $20\%$
  4. $25\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the $3rd$ number be $100$. Then,


$1st$ number $= 70$ and $2nd$ number $= 63$

$2nd$ number is less than 1st by $(\dfrac{7}{70}\times 100)=10 \%$