Tag: money and metric measures as percentage

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Questions Related to money and metric measures as percentage

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

If the price of sugar is increased by 25% today; by what percent should it be decreased tomorrow to bring the price back to the original?

  1. 25%

  2. 24%

  3. 22%

  4. 20%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the price of the sugar today be $ 100 $
Then its price tomorrow will be  $ 125 $

So,  to bring back the price to normal it should be decreased $ \cfrac {125-100}{125} \times 100 = 20 \%$

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

The sum of two numbers is $4000$. $10\%$ of one number is $\displaystyle 6\frac{2}{3}$ $\%$ of the other The difference of the number is

  1. $600$
  2. $800$
  3. $1025$
  4. $1175$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let one number be $x$. 

Then the other number $= 4000 - x$
Given, $10\%$ of $\displaystyle x=6\frac{2}{3}\%$ of $ (4000-x)$
$\displaystyle \Rightarrow \frac{10}{100}\times x=\frac{20}{3}\times \frac{1}{100}\times (4000-x)$
$\Rightarrow 10x=\dfrac{20}{3}\times 4000-\dfrac{20x}{3}$
$\displaystyle \Rightarrow 10x+\frac{20x}{3}=\frac{20}{3}\times 4000$
$\Rightarrow \dfrac{50x}{3}=\dfrac{20}{3}\times 4000$
$\displaystyle \Rightarrow x=\frac{20\times 4000}{50}=1600$
The two numbers are $1600$ and $2400$. 
$\displaystyle \therefore$ Their difference is $2400 - 1600 = 800$.

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

If p is 6 times that of q, what percent is q less than p?

  1. $12\, \displaystyle \frac{1}{2}\, \%$
  2. $83\, \displaystyle \frac{1}{3}\, \%$
  3. $6\, \displaystyle \frac{1}{4}\, \%$
  4. $33\, \displaystyle \frac{1}{3}\, \%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$p = 6q$
$p - q = 6q - q = 5q$
$\therefore$ q is less than p by $\displaystyle \frac{p\, -\, q}{p}\, \times\, 100\, \%$
$=\, \displaystyle \frac{5q}{6q}\, \times\, 100\, \%$ $=\, 83\, \displaystyle \frac{1}{3}\, \%$

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

If 'a' is  x % more than 'b' and 'b' is y % less than 'a'. then the relation between x and y is

  1. $\displaystyle \frac{1}{x}\, +\, \displaystyle \frac{1}{y}\, =\, \displaystyle \frac{1}{100}$
  2. $\displaystyle \frac{1}{y}\, -\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{1}{100}$
  3. $\displaystyle \frac{1}{x}\, -\, \displaystyle \frac{1}{y}\, =\, 100$
  4. $\displaystyle \frac{1}{y}\, -\, \displaystyle \frac{1}{x}\, =\, 100$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$y\, \%\, =\, \displaystyle \frac{100\, \times\, x}{100\, +\, x} \%$


$\Rightarrow y\, =\, \displaystyle \frac{100\, \times\, x}{100\, +\, x}$

$\Rightarrow \displaystyle \frac{1}{y}\, =\, \displaystyle \frac{100\, +\, x}{100\, \times\, x}\, =\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{1}{100}$

$\Rightarrow \displaystyle \frac{1}{y}\, -\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{1}{100}$

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

The % of total quantity represented by a $60^{circ}$ sector in a pie diagram is 

  1. $6 \displaystyle \frac{1}{4}$ %
  2. $16\, \displaystyle \frac{2}{3}$ %
  3. $11\, \displaystyle \frac{1}{9}$ %

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

$\displaystyle \frac{x}{100}\, \times\, 360\, =\, 60^{\circ}$


$x\, =\, 60\, \times\, \displaystyle \frac{100}{360}\, =\, \displaystyle \frac{100}{6}\, =\, 16\, \displaystyle \frac{2}{3}$ %

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

When the circumference of a circle decreases from $3\, \pi$ to $\pi$ , its area decreases by

  1. $16\, \displaystyle \frac{2}{3}$ %
  2. $66\, \displaystyle \frac{2}{3}$ %
  3. $88\, \displaystyle \frac{8}{9}$ %
  4. $12\, \displaystyle \frac{1}{2}$ %
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio of circumference = 3 : 1
Ratio of radii = 3 : 1
$\therefore$ ratio of areas $=\, 3^2\, : 1^2\, 9\, :\, 1$
% decrease in area $=\, \displaystyle \frac{8}{9}\, \times\, 100$
$=\, 88\, \displaystyle \frac{8}{9}$ %

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

Rajan earns $33\frac {1}{3}$ % less than Ram. Then by how much percent is Ram's income above Rajan's?

  1. 40%

  2. 50%

  3. 60%

  4. 70%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given that, Rajan earns $33\dfrac{1}{3}$ percent  less than Ram.


Let, the income of Ram is 100 r.s.


Then the income of Rajan is$=100-33\dfrac{1}{3}=100-\dfrac{100}{3}=\dfrac{200}{3}$


Difference in income is $=100-\dfrac{200}{3}=\dfrac{100}{3}$


Now, required income in percent $=\dfrac{100\times \dfrac{100}{3}}{\dfrac{200}{3}}=50\,$ percent


Hence, this is the answer. 

Multiple choice maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

$\displaystyle 12\frac{1}{2}$% of .......... = 35% of 700

  1. $490$
  2. $500$
  3. $1960$
  4. $1800$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the blank space be $x$ and we solve the given equality $12\dfrac { 1 }{ 2 }$% of $x=35$% of $700$ as follows:


$\dfrac { 12\dfrac { 1 }{ 2 }  }{ 100 } \times x=\dfrac { 35 }{ 100 } \times 700$

$ \Rightarrow \dfrac { \dfrac { 25 }{ 2 }  }{ 100 } \times x=35\times 7$

$ \Rightarrow \dfrac { 25 }{ 200 } \times x=245$

$ \Rightarrow \dfrac { x }{ 8 } =245$

$ \Rightarrow x=245\times 8$

$ \Rightarrow x=1960$

Hence, $12\dfrac { 1 }{ 2 }$% of $1960=35$% of $700$.