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 equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

The fraction $\dfrac {x}{y}$ is altered by decreasing $x$ by $25$ per cent and increasing $y$ by $25$ percent. The new fraction is what percent less than the original?

  1. 35

  2. 40

  3. 42

  4. 45
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the fraction is $=\dfrac{x}{y}$

If we decrease $x$ by $25\%$, then the $x=.75x$
If we increase $y$ by $25 \%$,  then the $y=1.25y$
$\therefore$ new fraction is $=\dfrac{.75x}{1.25y}=0.6\dfrac{x}{y}$
So, the new fraction is $0.4$ or $40\%$ less than the original fraction.

Multiple choice maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

Convert $\dfrac{16}{50}$ into percentage.

  1. $32\%$
  2. $34\%$
  3. $36\%$
  4. $38\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\Rightarrow$  We have to convert $\dfrac{16}{50}$ into percentage.

$\Rightarrow$  $\%=(\dfrac{16}{50}\times 100)\%$

$\Rightarrow$  $\%=(16\times 2)\%$

$\therefore$    $\%=32\%$

Multiple choice maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

Convert $\dfrac{14}{25}$ into percentage

  1. $55\%$
  2. $56\%$
  3. $57\%$
  4. $58\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  We have to convert $\dfrac{14}{25}$ into percentage.

$\Rightarrow$  $\%=(\dfrac{14}{25}\times 100)\%$

$\Rightarrow$  $\%=(14\times 4)\%$

$\therefore$    $\%=56\%$

Multiple choice maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

Convert $\dfrac{15}{50}$ into percentage

  1. $35\%$
  2. $30\%$
  3. $25\%$
  4. $20\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  We have to convert $\dfrac{15}{50}$ into percentage.

$\Rightarrow$  $\%=(\dfrac{15}{50}\times 100)\%$

$\Rightarrow$  $\%=(15\times 2)\%$

$\therefore$    $\%=30\%$

Multiple choice maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

In a survey, one in six people said they preferred a particular brand of cola. What this fraction is? And convert this fraction into percentage.

  1. $25\%$
  2. $17\%$
  3. $10\%$
  4. $5\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

One in six people means $\dfrac{1}{6}$ people in fraction.


To convert a fraction into percentage, multiply it by $100$
$\therefore \dfrac{1}{6} = \dfrac{1}{6} \times 100 = 16.67\% \approx 17\%$

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 $35\% $ of a number is $175$, then what percent of $175$ is that number ?

  1. $35\% $
  2. $65\% $
  3. $285.71\% $
  4. $420\% $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let the required number be $x$

It is given that $35$% of that number is $175$

=> $\dfrac { 35 \times  x }{ 100 } =175$

=> $x= \dfrac { 175 \times  100 }{ 35 }$

=> $x= 500$

Now, the question requires the percentage that $500$ is of that number

Let that percentage be $y \%$.

Now, $\dfrac { y \times  175 }{ 100 } =500$

=>$ y=\dfrac { 500 \times  100 }{ 175 } $

=>$ y = 285.714$

Hence the answer is $ 285.71\%$

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 $2\, \displaystyle \frac{1}{2}\, \%$ofa a number is 0.2, then what will be 120 % of it?

  1. 10.8

  2. 4.8

  3. 9.6

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

$2\, \displaystyle \frac{1}{2}\, \%$ of x = 0.2


$\displaystyle \frac{5}{200}\, \times\, x\, =\, 0.2$

$x\, =\, 0.2\, \times\, \displaystyle \frac{200}{5}\, =\, 8$

120 % of $8\, =\, \displaystyle \frac{120}{100}\, \times\, 8\, =\, 9.6$

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 $p _1\%$ of number $N _1$ is equal to $p _2\%$ of number $N _2$, what percent of $N _1$ is $N _2$?

  1. $\displaystyle\frac{100p _1}{p _2}$
  2. $\displaystyle\frac{100p _2}{p _1}$
  3. $\displaystyle\frac{p _1}{p _2}$
  4. $\displaystyle\frac{p _2}{p _1}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle\frac{p _1}{100}\times N _1=\frac{p _2}{100}\times N _2$

$\displaystyle\frac{N _1}{N _2}=\frac{p _2}{p _1}$, $\displaystyle N=\frac{p _2}{p _1}\times N _2$

Percent of $\displaystyle N _1=\left(\frac{p _2}{p _1}\times100\right)\%$ of $N _2$

Percent of $\displaystyle N _2=\left(\frac{p _2}{p _1}\times100\right)\%$ of $N _1$

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 $50$% of (x-y)=$30$% of $(x+y)$, then what percent of $x$ is $y$?

  1. $20$%
  2. $25$%
  3. $30$%
  4. $40$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$50\%$ of $(x-y)=30\% (x+y)$

$\dfrac{50}{100}(x-y)=\dfrac{30}{100}(x+y)$
$5(x-y)=3(x+y)$
$5x-3x=3y+5y$
$2x=8y$
$\Rightarrow x=4y \Rightarrow y=x/4$
To find : $\left[\dfrac{y}{x}\times 100\right]$
$\dfrac{y}{x}\times 100=\dfrac{x}{4}\times \dfrac{1}{x}\times 100 =\dfrac{100}{4}=25\%$
$\therefore y$ is $25\%$ of $x$

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

$12.5\% \,of\,192 = 50\% \,of\,?$ 

  1. $48$
  2. $96$
  3. $24$

  4. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$12.5\% \,\, of \,192 = 50\%$ of ?

First, we will find $12.5\%\,\, of\,\, 192$

$\Rightarrow \dfrac{x}{192}\times 100= 12.5$

$\Rightarrow x=\dfrac{12.5\times 192}{100}= 24$

Now we will find of what $50\%$ will give $24$

i.e., $\dfrac{24}{y}\times 100= 50$

$y = 48$