Tag: percent and percentage

Quizzes (7) Questions (44)

Questions Related to percent and percentage

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

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 $1.2\%$

  1. $1.2$
  2. $1.3$
  3. $1.3$
  4. $1.7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For parallel resistances, if each resistance has the same percentage error, the equivalent resistance inherits that same percentage error. With 1/R = 1/R₁ + 1/R₂ + 1/R₃, taking the differential shows that percentage error propagates directly when all resistances have identical % errors.

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

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

  1. $\;24\colon2\colon9$
  2. $\;2\colon9\colon24$
  3. $\;9\colon2\colon24$
  4. $\;9\colon24\colon2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

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

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?

  1. $\;\displaystyle\frac{8}{5}$
  2. $\;\displaystyle\frac{5}{8}$
  3. $\;\displaystyle\frac{12}{5}$
  4. $\;\displaystyle\frac{5}{7}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

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

  1. $100$ m
  2. $\dfrac{1}{100}$ m
  3. $1$ m
  4. $10$ m
  5. $\dfrac {10000}{m}$
Reveal answer Fill a bubble to check yourself
E Correct answer
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 $x= \cfrac{m}{100} \times y$
$\therefore y =\cfrac{k}{100} \times \cfrac{m}{100} \times y$
$k = \cfrac{10000}{m}$