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.

percentage calculationsfraction conversionspercentage increase problemsnumerator denominator changessuccessive percentages

Fractions and Percentages Questions

Multiple choice maths equivalent fractions comparing and ordering fractions comparing fractions fractions and its related operations

Which is the greatest number in the following

  1. $16\frac{2}{3}\% $
  2. $\frac{2}{{15}}$
  3. $\frac{1}{{11}}$
  4. $0.17$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$16 \dfrac 2 3 \% ; \dfrac{2}{15} ; \dfrac{1}{11} ; 0.17$

$\Rightarrow \dfrac{50}{3} \times \dfrac{1}{100} ; \dfrac{2}{15} ; 0.0909.... ; 0.17$

$\Rightarrow \dfrac{1}{3 \times 2} ; 0.1333 ; 0.0909 .... ; 0.17$

$\Rightarrow 0.1666...7 ; 0.1333 ; 0.0909 ; 0.17$

$\therefore 0.17$ is greater 
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. 

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

The total solar radiation proportion of PAR is

  1. Less than 50%

  2. More than 80%

  3. About 70%

  4. About 60%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sunlight is like a rain of photons of different frequencies. Visible light consists of radiations having a wavelength of 390-760 nm. Part of spectrum used in photosynthesis has a wavelength of 400-700 nm. It is called photosynthetically active radiation (PAR). The proportion of PAR of the total solar radiation is less than 50%. Only 2-10% of PAR is captured by the plants.

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 than 50 %
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Of the total incident solar radiation the proportion of PAR (photosynthetically active radiation) accounts to less than 50%. Photosynthetically active radiation designates the spectral range of solar radiation from 400 to 700 nanometers, that photosynthetic organisms are able to use in the process of photosynthesis.