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

What is 3/10 + 60/100?

  1. 90/100

  2. 63/100

  3. 63/10

  4. 90/10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

3/10 + 60/100 = 30/100 + 60/100 = 90/100.

Multiple choice

What is 8/10 + 2/100?

  1. 100/100

  2. 82/10

  3. 82/100

  4. 80/100
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

8/10 + 2/100 = 80/100 + 2/100 = 82/100.

Multiple choice

What is 3/10 + 40/100?

  1. 43/100

  2. 43/10

  3. 70/100

  4. 70/10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To add 3/10 and 40/100, convert 3/10 to 30/100. Adding 30/100 and 40/100 results in 70/100.

Multiple choice

Which fraction represent 3.25

  1. 3 25/100

  2. 3.25/10

  3. 30.5/10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The decimal 3.25 consists of a whole number 3 and 25 hundredths, which is 3 25/100.

Multiple choice

What is the fraction for 3/4?

  1. 34/10

  2. .75

  3. 3/4/10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The question asks for the decimal equivalent of 3/4. 3/4 equals 0.75, which is option B. Option A (34/10) would equal 3.4, not 0.75. Option C is not valid fraction notation. The question wording 'What is the fraction for 3/4?' is unclear; it should ask for the decimal form of 3/4.

Multiple choice biology natural resources and agriculture manure manures and fertilisers role of organic manures in soil management

A fertiliser has a formula of three figures $15-9-9$. They stand for percentage of.

  1. N, Ca and Mg

  2. Mg, P and K

  3. Ca, N and Fe

  4. N, P and K
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The three numbers on fertilizer represent the value of the three macro-nutrients used by plants. These macro-nutrients are nitrogen (N), phosphorus (P) and potassium (K) or NPK for short. NPK fertilizer is a complex fertilizer comprised primarily of the three primary nutrients required for healthy plant growth. Nitrogen is essential for green plant growth and enables plants to manufacture food from sunlight through photosynthesis. Phosphorus aids the plant in the earliest stages of development and facilitates the reproductive fruiting process. Potassium boosts plant vigour and disease and stress resistance.

So the correct option is ' N, P and K'.

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 calculated according to the expression
$Q =\dfrac{A^3B^3}{C\sqrt D}$
If percentage errors in $A, B, C, D$ are $2\%, 1\%, 3\%$ and $4\%$ respectively. What is the maximum percentage error in $Q$?

  1. $\pm\ 8\%$
  2. $\pm\ 10\%$
  3. $\pm\ 14\%$
  4. $\pm\ 12\%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Q = (A^3 * B^3) / (C * D^0.5). Error dQ/Q = 3*dA/A + 3*dB/B + dC/C + 0.5*dD/D. dQ/Q = 3(2%) + 3(1%) + 3% + 0.5(4%) = 6% + 3% + 3% + 2% = 14%.

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 a, b, c are $\pm 1$%, $\pm 3$% and $\pm 2$% respectively. The percentage error in $\dfrac{a^2}{bc^3}$ is:

  1. $\pm 13$%
  2. $\pm 9$%
  3. $\pm 6$%
  4. $\pm 11$%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let $Y=\dfrac { { a }^{ 2 } }{ b{ c }^{ 3 } } $
$\displaystyle \frac { \Delta Y }{ Y } \times 100=\pm \left( 2\times \frac { \Delta a }{ a } \times 100+\frac { \Delta b }{ b } \times 100+3\times \frac { \Delta c }{ c } \times 100 \right) $
                    $=\pm \left( 2\times 1+3+3\times 2 \right)$

                    $ =\pm 11$

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

Given $A=\dfrac{x^p}{y^qz^r}$. The percentage errors in measurement of $x, y$ and $z$ are 1 %, 0.5 % and 2% respectively. If $p=3, q=2$ and $r=1$ then the maximum percentage error in A is  

  1. $5$ %
  2. $6$ %
  3. $3$ %

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

Given, $A=\dfrac{x^p}{y^qz^r}$
Take ln and then differentiate , $\dfrac{\Delta A}{A}=\pm\left(p\dfrac{\Delta x}{x}+q\dfrac{\Delta y}{y}+r\dfrac{\Delta z}{z}\right)$
Thus the maximum percentage error in A:
$\dfrac{\Delta A}{A}\times 100=p\dfrac{\Delta x}{x}\times 100+q\dfrac{\Delta y}{y}\times 100+r\dfrac{\Delta z}{z}\times 100=(3\times 1)+(2\times 0.5)+(1\times 2)=6$ %

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 $S$ is given by $S = \dfrac {a^{2}b^{3}}{c\sqrt {d}}$.
If errors of measurements in $a, b, c, d$ are $4\%, 2\%, 3\%, 1\%$ respectively, find the percentage error in the value of $S$.

  1. $7.5\%$.
  2. $17.5\%$.
  3. $27.5\%$.
  4. $10.5\%$.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

S = (a^2 * b^3) / (c * d^0.5). dS/S = 2*da/a + 3*db/b + dc/c + 0.5*dd/d. dS/S = 2(4%) + 3(2%) + 3% + 0.5(1%) = 8% + 6% + 3% + 0.5% = 17.5%.

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

In an experiment four quantities a, b, c and d are measured with percentage error $1$ %, $2$%, $3$% and $4$% respectively. Quantity P is calculated as follows:
$P=\frac{ab^2}{\sqrt{cd^3}}$
Percentage error is P is

  1. $4$%
  2. $7$%
  3. $9$%
  4. $10$%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Quantity $P$ is calculated as follow $P = \frac{{a{b^2}}}{{\sqrt {c{d^3}} }}$

Formula of % error should be,
% error in $P=3 \times$%error in $a+2 \times $% error in $b+$%error in $c+$% error in d
Given,
% error in $a=1$%
% error in $b=2$%
% error in $c=3$%
% error in $d=4$%
Hence,
% error in $P=3 \times 1+2 \times 2+3+4$
$=3$%-$4$%+$3$%+$4$%
$=10$%
$\therefore $ Option $D$ is correct answer.

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

Given $x=\dfrac {ab^2}{c^3}$, if the percentage errors in a, b and c are $\pm$ 1%, $\pm$ 3% and $\pm$ 2% respectively, the percentage error in $x$ can be:

  1. $\pm$ 13%
  2. $\pm$ 7%
  3. $\pm$ 18%
  4. $\pm$ 19%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The given quantity is   $x = \dfrac{ab^2}{c^3}$
Maximum percentage error in $x$ is   $\dfrac{\Delta x}{x}\times 100 = [\dfrac{\Delta a}{a}+2\dfrac{\Delta b}{b}+3\dfrac{\Delta c}{c}]\times 100$
$\dfrac{\Delta x}{x}\times 100 = [1+2\times 3+3\times 2] = \pm 13$ %

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 P is repleted to four observed a,b,c,d as follows: $P=\dfrac{a^3b^2}{\left(\sqrt c.d\right)}$ The percentage errors in the measurement of a,b,c and d are $1\%3\%,4\%$ and $2\%$ respectively. The percentage error in the quantity P is

  1. $7\%$
  2. $9\%$
  3. $11\%$
  4. $13\%$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
$P=\dfrac { { a }^{ 3 }{ b }^{ 2 } }{ \sqrt { cd }  } $

$\dfrac { \Delta P }{ P } =\dfrac { 3\Delta a }{ a } +\dfrac { 2\Delta b }{ b } +\dfrac { 1 }{ 2 } \dfrac { \Delta c }{ c } +\dfrac { \Delta d }{ d } $

$\left( \dfrac { \Delta P }{ P } \times 100 \right) $% $=\left( 3\times \dfrac { \Delta a }{ a } \times 100+2\times \dfrac { \Delta b }{ b } \times 100+\dfrac { 1 }{ 2 } \times \dfrac { \Delta c }{ c } \times 100+\dfrac { \Delta d }{ d } \times 100 \right) $%
                              $=3\times 1+2\times 3+\dfrac { 1 }{ 2 } \times 4+2$
                              $=3+6+2+2=13$%
Percentage error $=13$%