Tag: maths

Questions Related to maths

If $50$% of (x-y)=$30$% of $(x+y)$, then what percent of $x$ is $y$?

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. $25$%

  3. $30$%

  4. $40$%

Show answer
Correct Option: B
Explanation:

$50\%$ of $(x-y)=30\% (x+y)$

$\dfrac{50}{100}(x-y)=\dfrac{30}{100}(x+y)$
$5(x-y)=3(x+y)$
$5x-3x=3y+5y$
$2x=8y$
$\Rightarrow x=4y \Rightarrow y=x/4$
To find : $\left[\dfrac{y}{x}\times 100\right]$
$\dfrac{y}{x}\times 100=\dfrac{x}{4}\times \dfrac{1}{x}\times 100 =\dfrac{100}{4}=25\%$
$\therefore y$ is $25\%$ of $x$

$12.5\% \,of\,192 = 50\% \,of\,?$ 

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

  1. $48$

  2. $96$

  3. $24$

  4. none of these

Show answer
Correct Option: A
Explanation:
$12.5\% \,\, of \,192 = 50\%$ of ?

First, we will find $12.5\%\,\, of\,\, 192$

$\Rightarrow \dfrac{x}{192}\times 100= 12.5$

$\Rightarrow x=\dfrac{12.5\times 192}{100}= 24$

Now we will find of what $50\%$ will give $24$

i.e., $\dfrac{24}{y}\times 100= 50$

$y = 48$

$45$ is what percent of $54$ ?

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

  1. $81$%

  2. $83$%

  3. $85$%

  4. None of these

Show answer
Correct Option: D
Explanation:

Percentage = $\dfrac {45}{54}$ $\times 100$

= $\dfrac {5}{6}$ $\times 100$  (removing common factor 9)

= $\dfrac {500}{6}$

= $\dfrac {250}{3}$

= $83\dfrac{1}{3}$%

Out of 800 oranges, 50 are rotten. Find the percentage of good oranges.

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

  1. $\displaystyle\,7\,\frac{1}{4}\%$

  2. $\displaystyle\,93\,\frac{1}{4}\%$

  3. $\displaystyle\,93\,\frac{3}{4}\%$

  4. $\displaystyle\,7\,\frac{3}{4}\%$

Show answer
Correct Option: C
Explanation:

Good oranges are $ 800 - 50 = 750 $
So, percentage of good oranges $ = \cfrac { 750}{800} \times 100 $ %  $ = \cfrac {375}{4} $ % $ = 93 \cfrac {3}{4} $ %

A's income is 25% more than B's. Find, B's income is how much percent less than A'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. $25\%$

  2. $22.5\%$

  3. $20\%$

  4. $30\%$

Show answer
Correct Option: C
Explanation:

Let B's income be $ 100 $
Then A's income is $ 125 $
So,  B's income is $ \cfrac {125-100}{125} \times 100 = 20 \%$ less than of A.

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%

Show answer
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%

Show answer
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. $1175$

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

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

Show answer
Correct Option: B
Explanation:

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


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

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

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