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 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

Which is the greatest ?

  1. $\dfrac{50}{3}\%$
  2. $\dfrac{2}{15}$
  3. $0.17$
  4. $6\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Option A$\Rightarrow \begin{pmatrix}\dfrac{50}{3}\end{pmatrix}\times\begin{pmatrix}\dfrac{1}{100}\end{pmatrix}=\dfrac{1}{6}=0.166$
Option B $\Rightarrow \dfrac{2}{15}=0.133$
Option C $\Rightarrow 6\%=\dfrac{6}{100}=0.06$
Clearly $\Rightarrow 0.17$ is greater

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 $(\dfrac{7}{70}\times 100)=10 \%$

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

$83.33\% $ of coins out of $36$ coins are $20$ paise coins and rest are $10$ paise coins which amounts to $6.60$. Find the number of $10$ paise coins.

  1. $8$
  2. $5$
  3. $6$
  4. $2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given : $83.33$% of $36$ coins are $20$ paisa coins

$83.33$% of $36 =\left( \cfrac { 83.33 }{ 100 }  \right) \times 36=30$

So, $30$ coins are $20$ paise coins and remaining $(36-30)= 6$ coins are $10$ paise coins.

Value $=30\times 20+6\times 10=660$ Paise $=Rs. 6.60$, which is the given amount.

$\therefore $ Number of $10$ paise coins are $6$.

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

Convert the following percents into fractions:

$33\dfrac{1}{3}\%$

  1. $\dfrac{99}{100}$
  2. $\dfrac{3}{100}$
  3. $\dfrac{33}{100}$
  4. $\dfrac{1}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given percent  $={33}\dfrac{1}{3}\%$

Now, ${33}\dfrac{1}{3}=\dfrac{(33\times3)+1}{3}=\dfrac{100}{3}$
${33}\dfrac{1}{3}\%=\dfrac {100}{3}\times\dfrac{1}{100}=\dfrac {1} {3}$

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

Convert the following percents into fractions:

$6\dfrac{1}{4}\%$

  1. $\dfrac{2}{16}$
  2. $\dfrac{1}{16}$
  3. $\dfrac{25}{4}$
  4. $\dfrac{1}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given percent $={6}\dfrac{1}{4}\%$
Now, ${6}\dfrac{1}{4}=\dfrac{(6\times4)+1}{4}$
                 $=\dfrac{25}{4}$
$\implies{6}\dfrac{1}{4}\%=\dfrac {25}{4}\times\dfrac{1}{100}$
                      $=\dfrac {1} {16}$
Multiple choice maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

Convert the following percents into fractions:
$8\dfrac{1}{3}\%$

  1. $\dfrac{1}{12}$
  2. $\dfrac{25}{3}$
  3. $\dfrac{2}{75}$
  4. $\dfrac{3}{25}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given percent : ${8}\dfrac{1}{3}\%$

${8}\dfrac{1}{3}=\dfrac{(8\times3)+1}{3}=\dfrac{25}{3}$

${8}\dfrac{1}{3}\%=\dfrac {25}{3}\times\dfrac{1}{100}=\dfrac {1} {12}$
Multiple choice maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

$16\frac{2}{3}\% $ of $600$gm $ - 33\frac{1}{3}\% $ of $180$gm

  1. $20$ gm
  2. $30$ gm
  3. $40$ gm
  4. $60$ gm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$16 \dfrac{2}{3}\%$ of $600\ gm-33 \dfrac{1}{3} \%$ of $180\ gm$
$\Rightarrow \left[ \dfrac{50}{3} \times \dfrac{1}{100} (600)- \left( \dfrac{100}{3} \times \dfrac{1}{100} \right) (180) \right] gm$
$\Rightarrow \left[ \dfrac{600}{6}- \dfrac{180}{3} \right]\ gm$
$\Rightarrow (100-60)\ gm$
$\Rightarrow 40\ gm$
$\therefore [16 2/3 \% \ of\ 600\ gm-33 1/3 \% \ of\ 180\ gm]=40\ gm$