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 physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

A physical quantity $Q$ is released to four observable $x,y,z$ and $t$  by the relation
$Q=\dfrac {x^{2/5}z^{3}}{y\sqrt {t}}$ 
The percentage errors of measurement in $x,y,z$ and $t$ are $2.5\%,2\%,0.5\%$ and $1\%$ receptively. The percentage error in $Q$ will be

  1. $5\%$
  2. $4.5\%$
  3. $8\%$
  4. $7.75\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The relative error in Q is given by (dQ/Q) = (2/5)(dx/x) + (dy/y) + 3(dz/z) + (1/2)(dt/t). Substituting the given percentages: (2/5)*2.5% + 2% + 3*0.5% + (1/2)*1% = 1% + 2% + 1.5% + 0.5% = 5%.

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

A physical quantity A is dependent on other four physical quantities p, q, r and s as given by $\displaystyle A= \frac{\sqrt{pq}}{r^{2}s^{3}}.$ The percentage error of measurement in p, q, r and s are 1%, 3%, 0.5% and 0.33% respectively, then the maximum percentage error in A is :

  1. 2%

  2. 0%

  3. 4%

  4. 3%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using formula for error analysis:
$\dfrac{ \Delta A}{A} = \dfrac{1}{2} \dfrac{ \Delta p}{p}+ \dfrac{1}{2} \dfrac{ \Delta q}{q} + 2  \dfrac{ \Delta r}{r} + 3 \dfrac{ \Delta s}{s}= \dfrac{1}{2} \times 1 + \dfrac{1}{2} \times 3 + 2 \times 0.5 + 3 \times 0.33= 4$
Hence, percentage of error is 4%

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

If $X=a-b$, then the maximum percentage error in the measurement of $x$ will be:

  1. $\left (\dfrac {\Delta a}{a}+\dfrac {\Delta b}{b}\right )\times 100\%$
  2. $\left (\dfrac {\Delta a}{a}-\dfrac {\Delta b}{b}\right )\times 100\%$
  3. $\left (\dfrac {\Delta a}{a-b}+\dfrac {\Delta b}{a-b}\right )\times 100\%$
  4. $\left (\dfrac {\Delta a}{a-b}-\dfrac {\Delta b}{a-b}\right )\times 100\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Maximum absolute error is $\Delta a+\Delta b$.
Therefore the percentage error $=\dfrac {\text {absolute error}}{\text {actual error}}\times 100$
$\therefore$ Percentage error $= \left (\dfrac {\Delta a}{a-b}+\dfrac {\Delta b}{a-b}\right )\times 100$%

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

An experiment measures quantities x, y, z and then t is calculated from the data as $t\, =\, \displaystyle \frac{xy^2}{z^3}$. If percentage errors in x, y and z are respectively 1 %, 3 %, 2 %, then percentage error in t is

  1. 10 %

  2. 4 %

  3. 7 %

  4. 13 %
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
The given quantity is   $t = \dfrac{xy^2}{z^3}$
Percentage error in $t$ is given by    $\dfrac{\Delta t}{t}\times 100  =1\times(\dfrac{\Delta x}{x}\times 100)+2(\dfrac{\Delta y}{y}\times 100)+3(\dfrac{\Delta z}{z}\times 100)$
$\implies \ \dfrac{\Delta t}{t}\times 100 = 1\times 1+2\times 3+3\times 2 = 13$%
Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The percentage error in the measurement of a quantity Z which is related to two other quantities as Z = $\displaystyle x^{-1}y^{+1}$ is due to the percentage error in the measurement of x and y which are 2% and 1% respectively. Find the maximum fractional error in Z (in %).

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The quantity is given as      $Z = \dfrac{y}{x}$

$\therefore      \dfrac{\Delta Z}{Z}  \times 100  =  \dfrac{\Delta x}{x} \times 100   +  \dfrac{\Delta y}{y}   \times 100$
$\implies         \dfrac{\Delta Z}{Z}  \times 100  =  2+1  = 3$
Thus percentage error in Z is equal to  $3$%.

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The percentage errors in quantities $P, Q, R$ and $S$ are $0.5$%, $1$%, $3$% and $1.5$% respectively in the measurement of a physical quantity $A = \dfrac {P^{3}Q^{2}}{\sqrt {R}S}$.
The maximum percentage error in the value of $A$ will be

  1. $8.5\%$
  2. $6.0\%$
  3. $7.5\%$
  4. $6.5\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Percentage error $\dfrac{\Delta A}{A} \times 100 = 3 \dfrac{\Delta P}{P} \times 100 + 2 \dfrac{\Delta Q}{Q} + \dfrac{1}{2} \dfrac{\Delta R}{R} \times 100 + \dfrac{\Delta S}{S} \times 100$ 

$ = 3 \times 0.5 + 2 \times 1+ 0.5 \times 3 + 1.5 = 6.5 %$

Multiple choice statistics data handling analysis bar charts frequency table and diagrams bar diagram

Frequency of a variable is always _______.

  1. <ul><li dir="ltr"><p dir="ltr">a digit</p></li></ul>

  2. a fraction

  3. an integer

  4. in percentage
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Frequency represents the count of occurrences for a particular value or interval. Since you cannot have a fraction of an occurrence, frequencies are always expressed as whole numbers, or integers.

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

$\left (1 - \dfrac {1}{2}\right ) + \left (\dfrac {3}{4} - \dfrac {1}{4}\right )=$

  1. $0$
  2. $1$
  3. $\dfrac {1}{2}$
  4. $\dfrac {3}{4}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$\left ( 1-\dfrac{1}{2} \right )+\left ( \dfrac{3}{4}-\dfrac{1}{4} \right )$
$=\left ( \dfrac{2-1}{2} \right )+\left ( \dfrac{3-1}{4} \right )$
$=\dfrac{1}{2}+\dfrac{2}{4}= \dfrac{1}{2}+\dfrac{1}{2}= 1$
Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

Which of the following are true?

(a) $\displaystyle \frac{35}{16}=2.1875$
(b) $\displaystyle \frac{17}{8}=2.125$
(c) $\displaystyle \frac{327}{500}=0.654$
(d) $\displaystyle \frac{14588}{625}=23.3408$

  1. $a,b,c,d$
  2. $a,c,d$
  3. $a,b,c$
  4. $a,b,d$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(i) $\displaystyle \frac{35}{16} = \frac{35 \times 5^4}{2 \times 5^4}= \frac{35 \times 625}{(10)^4}= \frac{21875}{10000}=2.1875$
(ii) $\displaystyle \frac{17}{8} = \frac{17 \times 5^3}{2^3 \times 5^3} = \frac{17 \times 125}{(10)^3}=\frac{2125}{1000}=2.125$
(iii) $\displaystyle \frac{327}{500} = \frac{327}{5\times 5 \times 5 \times 2 \times 2}$
$=\displaystyle \frac{327}{5^3 \times 2^2} = \frac{327}{5^3 \times 2^3}= \frac{654}{(10)^3} = 0.654$
(iv) $\displaystyle \frac{14588}{625} = \frac{2^2 \times 7 \times 521}{5^4} = \frac{2^6 \times 7 \times 521}{2^4 \times 5^4}$
$\displaystyle =\frac{233408}{10^4}=23.3408$

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

The fraction equivalent to $\displaystyle \frac {1}{2}$ is

  1. $\displaystyle \frac {2}{4}$
  2. $\displaystyle \frac {3}{6}$
  3. $\displaystyle \frac {8}{16}$

  4. All the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {1\, \times\, 2}{2\, \times\, 2}\, =\, \displaystyle \frac {2}{4}$


$\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {1\, \times\, 3}{2\, \times\, 3}\, =\, \displaystyle \frac {3}{6}$

$\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {1\, \times\, 8}{2\, \times\, 8}\, =\, \displaystyle \frac {8}{16}$

So $\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {2}{4}\, =\, \displaystyle \frac {3}{6}\, =\, \displaystyle \frac {8}{16}$

Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

The fraction equivalent to $\displaystyle \frac {1}{2}$ is .......... 

  1. $\displaystyle \frac {3}{6}$
  2. $\displaystyle \frac {5}{10}$
  3. $\displaystyle \frac {9}{8}$

  4. All the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac {1}{2}\, =\, \displaystyle \frac {3}{6}\, =\, \displaystyle \frac {5}{10}\, =\, \displaystyle \frac {9}{18}$