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 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 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 $20$.
Multiple choice maths the trapezium rule approximation errors and approximations the need for approximation

If the percentage error in the edge of a cube is 1, then error in its volume is

  1. $1 \%$
  2. $2 \%$
  3. $3 \%$

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Volume of cube $V=x^{3}$
$\Rightarrow \displaystyle \dfrac{dV}{dx}=3x^{2}$
Percentage error in x is 1%.
$\Rightarrow \displaystyle \dfrac{\Delta x}{x}=\dfrac{1}{100}$
$\Rightarrow \displaystyle \Delta x=\dfrac{x}{100}$
Approximate error in V $\displaystyle=dV=(\dfrac{dV}{dx}) \Delta x$
                                  $\displaystyle = \dfrac{3{x}^{3}}{100}$                              
Percentage error in V $\displaystyle= \dfrac{dV}{V} $
                                   $\displaystyle=\dfrac{3}{100}=3\%$
Multiple choice maths the trapezium rule approximation errors and approximations the need for approximation

If error in  measuring the edge of a cube is $k$% then the percentage error in estimating its volume is

  1. $k$
  2. $3k$
  3. $\displaystyle \frac{k}{3}$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the actual length of the cube be a.

Therefore the measured length of the cube will be 
$=a(1\pm0.0k)$
$=a(1\pm\dfrac{k}{100})$
Considering positive error, 
$a'=a(1+\dfrac{k}{100})$
$V'=a^{3}(1+\dfrac{k}{100})^{3}$

$=a^{3}(1+3(\dfrac{k}{100})+3(\dfrac{k}{100})^{2}+(\dfrac{k}{100})^{3})$

Since $\dfrac{k}{100}<<1$, hence we neglect the higher order terms.
Thus 
$V'=a^{3}(1+3(\dfrac{k}{100}))$

Actual volume V
$V=a^{3}$
Therefore 
$V'-V=a^{3}(1+\dfrac{3k}{100})-a^{3}$

$=a^{3}(\dfrac{3k}{100})$

$\dfrac{V'-V}{V}=\dfrac{a^{3}\dfrac{3k}{100}}{a^{3}}$

$=\dfrac{3k}{100}$

$=\dfrac{3k}{100}$

$\dfrac{V'-V}{V}\times 100=3k$
Therefore percentage error in volume is $3k$.

Multiple choice maths the trapezium rule approximation errors and approximations the need for approximation

The percentage error in the $11^{th}$ root of the number $28$ is approximately ____________ times the percentage error in $28$

  1. $\dfrac { 1 }{ 28 } $
  2. $\dfrac { 1 }{ 11 } $
  3. $11$
  4. $28$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Suppose $y = x^{11}$

$dy = 11x^{10}dx$
Dividing by y on both sides, we have $ \cfrac{\Delta y}{y} = \cfrac{11x^{10}\Delta x}{y} = \cfrac{11x^{10}\Delta x}{x^{11}}$
$\therefore \cfrac{\Delta y}{y} = \cfrac{11 \Delta x}{x}$

Here, when $y = 28$, $x$ will be the $11^{th}$ root of $28$.
$\therefore \cfrac{\Delta (28)}{28} = \cfrac{11 \Delta (\sqrt[11]{28})}{\sqrt[11]{28}}$
Hence, the percentage error in the $11$th root of $28$ would approximately be $\cfrac{1}{11}$ times the error in $28$

Multiple choice evs - i substances, objects and energy renewable and non-renewable resources renewable and non-renewable sources of energy solar energy and its applications renewable resources alternative fuels and energy sources alternative sources of energy

What is the percentage of ${92} _U^{235} in \,92 _U^{238}$?

  1. 0.2%

  2. 0.7%

  3. 98%

  4. 100%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Natural uranium consists of about 99.3% U-238 and only about 0.7% U-235. The question asks for the percentage of U-235 in natural uranium.

Multiple choice biology modern agriculture modern equipments in agriculture soil quality methods of crop production

What is the percentage of carbon in wrought iron?

  1. 0.05-1%

  2. 1-2%

  3. 2-3%

  4. 3-4%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Wrought iron is a tough malleable form of iron with a very low carbon content (0.05-1%). It is very soft, ductile, magnetic and has very high tensile strength. It can easily be converted into different shapes. 
So the correct option is '0.05-1%'.
Multiple choice biology ecology carbon cycling mineral coal carbon cycle

The percentage of carbon in lignite is ______%.

  1. $70\, to \,90$
  2. $60\, to\, 80$
  3. $60\, to\, 90$
  4. $60\, to \,70$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Lignite is brownish-black in color and has a carbon content around   60–70  percent, a high inherent moisture content sometimes as high as $75$ percent, and an ash content ranging from $6–19$ percent.

Multiple choice botany ecosystem energy flow in food chain food chain and energy flow energy flow in ecosystem

Of the total incident solar radiation the proportion of PAR is

  1. More than 80%

  2. About 70%

  3. About 60%

  4. Less then 50%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Source of energy in an ecosystem is solar energy. 50 per cent of the solar energy incident over Earth is present in PAR (photosynthetically active radiation). Almost 1 to 5 percent of incident solar energy or 2 to 10 percent of PAR is captured by photosynthetic organisms in synthesis of organic matter.