Tag: percent and percentage

Questions Related to percent and percentage

The possible percentage error in computing the parallel resistance $R$ of three resistances $R _{1},R _{2},R _{3}$ from the formula $\dfrac {1}{R}=\dfrac {1}{R _{1}}+\dfrac {1}{R _{2}}+\dfrac {1}{R _{3}}$, if $R _{1},R _{2},R _{3}$ are each by $1.2\%$

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $1.2$

  2. $1.3$

  3. $1.3$

  4. $1.7$

Show answer
Correct Option: A

If $33\displaystyle\frac{1}{3}\%$ of $A=1.5$ of $B=\displaystyle\frac{1}{8}$ of $C$, then $A\colon\,B\colon\,C$ is

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $\;24\colon2\colon9$

  2. $\;2\colon9\colon24$

  3. $\;9\colon2\colon24$

  4. $\;9\colon24\colon2$

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Correct Option: C
Explanation:

$\;\displaystyle\frac{100}{3\times100}\times\,A=\displaystyle\frac{3}{2}\times\,B=\displaystyle\frac{1}{8}\times\,C=x\,(say)$
$\;\;\;\;\;\Rightarrow\;A=3x,\,B=\displaystyle\frac{2}{3}x,\,C=8x$
$\;\;\;\;\;\;\Rightarrow\;A\colon\,B\colon\,C=3\colon\displaystyle\frac{2}{3}\colon8=9\colon2\colon24$.

If the numerator of a fraction is increased by $300\%$ and the denominator is increased by $500\%$, the resultant fraction is $\displaystyle\frac{5}{12}$. What was the original fraction?

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $\;\displaystyle\frac{8}{5}$

  2. $\;\displaystyle\frac{5}{8}$

  3. $\;\displaystyle\frac{12}{5}$

  4. $\;\displaystyle\frac{5}{7}$

Show answer
Correct Option: B
Explanation:

Let the original fraction be $\dfrac {p}{q}$. 

Then, $\displaystyle\frac{p+\displaystyle\frac{300}{100}P}{q+\displaystyle\frac{500}{100}P}=\displaystyle\frac{5}{12}$
$\Rightarrow \displaystyle\frac{4p}{6q}=\displaystyle\frac{5}{12}$
$\Rightarrow\;\displaystyle\frac{p}{q}=\displaystyle\frac{5}{12}\times\displaystyle\frac{6}{4}=\displaystyle\frac{5}{8}$

Half of $1$ percent written as a decimal is

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $0.2$

  2. $0.02$

  3. $0.05$

  4. $0.005$

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Correct Option: D
Explanation:

Half of $ 1\%$ in decimals

It will be $\displaystyle \frac {1}{2} \times 1 \% = \displaystyle \frac {1}{2}\times  \frac {1}{100}$
$ = \displaystyle \frac {1}{200}= 0.005$

What percentage is equivalent to $\dfrac {3}{8}$ ?

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $33.33\%$

  2. $39\%$

  3. $37.5\%$

  4. $40\%$

Show answer
Correct Option: C
Explanation:
$\dfrac {3}{8}$ can be written in percentage form as:
Equivalent percentage  $= \dfrac {(3 \times 100)}{8} = 37.5\%$
So, option C is correct.

If $m > 0$ and $x$ is $m$ percent of $y$, then in terms of $m$, $y$ is what percent of $x$ ? 

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $100$ m

  2. $\dfrac{1}{100}$ m

  3. $1$ m

  4. $10$ m

  5. $\dfrac {10000}{m}$

Show answer
Correct Option: E
Explanation:

Given that : x is $m\%$ of y

$\Rightarrow x = \cfrac{m}{100} \times y$ 
Now, let's say that y is $k\%$ of x, then
$y = \dfrac{k}{100} \times x$
But $x= \cfrac{m}{100} \times y$
$\therefore y =\cfrac{k}{100} \times \cfrac{m}{100} \times y$
$k = \cfrac{10000}{m}$

Express $0.08\%$ as a fraction

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $\dfrac{1}{250}$

  2. $\dfrac{1}{1250}$

  3. $\dfrac{1}{125}$

  4. $\dfrac{1}{25}$

Show answer
Correct Option: B
Explanation:

$0.08\%$ can be written as $\dfrac{0.08}{100}$

$=\dfrac{8}{10000}$
$=\dfrac{1}{1250}$
Hence, option B is correct.

Express the following as fraction and simplify:

$8 \%$

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $0$

  2. $\cfrac {1}{25}$

  3. $\cfrac {2}{25}$

  4. $\cfrac {4}{25}$

Show answer
Correct Option: C
Explanation:

To convert a percent to a fraction, write it over a denominator of 100 and simplify:
$8\% = \cfrac{8}{100} = \cfrac{2}{25}$

Convert $75$% to a fraction

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $2/3$

  2. $3/4$

  3. $4/5$

  4. None

Show answer
Correct Option: B
Explanation:

$75$%$=\cfrac{75}{100}=\cfrac{3}{4}$

Square root of $64$% is?

maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

  1. $0.8$

  2. $0.72$

  3. $0.74$

  4. $0.76$

Show answer
Correct Option: A
Explanation:

We have, $\sqrt{64\%}$


$\Rightarrow$  $\sqrt{\dfrac{64}{100}}$

$\Rightarrow$  $\dfrac{8}{10}$

$\Rightarrow$   $0.80$

$\therefore$    Square root of $64\%$ is $0.8.$