Tag: converting between fractions or decimals and percentages

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Questions Related to converting between fractions or decimals and percentages

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

15% of 10% of 20% of 1000 is 

  1. $1.50$
  2. $67$
  3. $150$
  4. $3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$15\%$ of $10\%$ of $20\%$ of $1000$


$\Rightarrow 15\%$ of $10\%\left[\dfrac{20}{100}\times 1000\right]$

$\Rightarrow 15\%$ of $10\%$ of $200$

$\Rightarrow 15\%\left[\dfrac{10}{100}\times 200\right]$

$\Rightarrow 15\%$ of $20$

$\Rightarrow \dfrac{15}{100}\times 20$

$\Rightarrow  3$

$\therefore\ 15\%$ of $10\%$ of $20\%$ of $1000=3$

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

If $40$%of a number is equal to two-third of another number, what is the ratio of first number to the second numbers?

  1. 2:5

  2. 3:7

  3. 5:3

  4. 7:3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$(l-m) (lm+l+x^{2})=0$
 Let the number be $x _{1} y$
Given :- $40\% $ of $(x) = \dfrac{2}{3}$ of $(y)$
to find :-$\dfrac{x}{y}= ?$
$\dfrac{40}{100} \times x = \dfrac{2}{3} \times y$
$\dfrac{x}{y}= \dfrac{2}{3} \times \dfrac{100}{40}$
$\Rightarrow \dfrac{x}{y}= \dfrac{5}{3}$
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 $x= \cfrac{m}{100} \times y$
$\therefore y =\cfrac{k}{100} \times \cfrac{m}{100} \times y$
$k = \cfrac{10000}{m}$