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 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

If a number is increased by 20%, what is the percentage decrease required to bring it back to its original value?

  1. 16.67%

  2. 20%

  3. 25%

  4. 33.33%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the original number be x. Increased number = x + 20% of x = x + 0.2x = 1.2x Percentage decrease required = (Increased number - Original number) / Increased number x 100% = (1.2x - x) / 1.2x x 100% = 0.2x / 1.2x x 100% = 20%.

Multiple choice

What is the coinsurance for Medicare Part A?

  1. 20%

  2. 30%

  3. 40%

  4. 50%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Medicare Part A coinsurance is 20% of the Medicare-approved amount for covered services.

Multiple choice

What is the coinsurance for Medicare Part B?

  1. 20%

  2. 30%

  3. 40%

  4. 50%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Medicare Part B coinsurance is 20% of the Medicare-approved amount for covered services.

Multiple choice

What is the success rate of root canal treatment?

  1. Over 90%

  2. Around 50%

  3. Less than 20%

  4. It varies widely depending on the individual case.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Root canal treatment boasts a high success rate, with over 90% of treated teeth functioning effectively for many years.

Multiple choice

What is the typical sugar content of maple syrup?

  1. 30-40%

  2. 50-60%

  3. 60-70%

  4. 70-80%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Maple syrup typically contains between 60% and 70% sugar.

Multiple choice

What is the coinsurance for Medicare Part A?

  1. 20%

  2. 25%

  3. 30%

  4. 35%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The Medicare Part A coinsurance for 2023 is 20%.

Multiple choice

What is the typical cocoa content of dark chocolate?

  1. 35-50%

  2. 50-70%

  3. 70-85%

  4. 85-100%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Dark chocolate typically has a cocoa content of 70-85%.

Multiple choice

What is the typical sugar content of ice cream?

  1. 10-12%

  2. 14-16%

  3. 18-20%

  4. 22-24%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The typical sugar content of ice cream is 18-20%.