Tag: expressing one quantity as a percentage of another

Questions Related to 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?

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

  1. 25%

  2. 24%

  3. 22%

  4. 20%

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Correct Option: D
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 \%$

Mona is 20% younger than Neetu. How much percent is Neetu older than Mona ?

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

  1. 20%

  2. 16%

  3. 25%

  4. 15%

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Correct Option: C
Explanation:

Let Neetu's age  be $ x $ years
Then Mona's age is $ 0.8x$  years

So,  Neetu is $ \cfrac {x-0.8x}{0.8} \times 100 = 25 \%$ older than Mona.

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

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

  1. $600$

  2. $800$

  3. $1025$

  4. $1175$

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Correct Option: B
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 $2400 - 1600 = 800$.

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

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

  1. $12\, \displaystyle \frac{1}{2}\, \%$

  2. $83\, \displaystyle \frac{1}{3}\, \%$

  3. $6\, \displaystyle \frac{1}{4}\, \%$

  4. $33\, \displaystyle \frac{1}{3}\, \%$

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Correct Option: B
Explanation:

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

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

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

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

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Correct Option: B
Explanation:

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


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

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

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

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

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

  1. $6 \displaystyle \frac{1}{4}$ %

  2. $16\, \displaystyle \frac{2}{3}$ %

  3. $11\, \displaystyle \frac{1}{9}$ %

  4. None

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Correct Option: B
Explanation:

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


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

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

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

  1. $16\, \displaystyle \frac{2}{3}$ %

  2. $66\, \displaystyle \frac{2}{3}$ %

  3. $88\, \displaystyle \frac{8}{9}$ %

  4. $12\, \displaystyle \frac{1}{2}$ %

Show answer
Correct Option: C
Explanation:

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

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

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

  1. 40%

  2. 50%

  3. 60%

  4. 70%

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Correct Option: B
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. 

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

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

  1. $490$

  2. $500$

  3. $1960$

  4. $1800$

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Correct Option: C
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 $700$.

$16$ is what percent of $12$?

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

  1. $133.33$%

  2. $100$%

  3. $120$%

  4. $150$%

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Correct Option: A
Explanation:

$\cfrac{16}{12}=\cfrac{Percent}{100}$

$Percent=\cfrac{16}{12}\times 100$
$\cfrac{400}{3}=133.33$%