Tag: maths

Questions Related to maths

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

Show answer
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%

Show answer
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. $1800$

Show answer
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. $150$%

Show answer
Correct Option: A
Explanation:

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

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

If $30\%$ of $140=x\%$ of $840$, then the value of $x$ 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. $5$

  2. $15$

  3. $24$

  4. $60$

Show answer
Correct Option: A
Explanation:

Given that $30\%$ of $140$ $=$ $x\%$ of $840$

Thus $\dfrac {30}{100}\times 140=\dfrac {x}{100}\times 840$
$\Rightarrow 42=8.4x$
$\Rightarrow x=5$

What is $25\%$ of $25\%$?

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

  1. $6.25$

  2. $0.625$

  3. $0.0625$

  4. $0.00625$

Show answer
Correct Option: C
Explanation:

We need to find $25\%$ of $25\%$

We know $25\%=\dfrac {25}{100}=0.25$
Thus $25\%$ of $0.25$ is equal to
$=\dfrac {25}{100}\times 0.25$
$=0.0625$
Hence, option C is correct.

If $p$ is $95\%$ of $q$, then what percentage of $p$ is $q$?

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

  1. 105%

  2. 105.3%

  3. 110%

  4. 115%

Show answer
Correct Option: B
Explanation:

$p=\cfrac{95q}{100}$

$\therefore \cfrac{q}{p} \times 100 = \cfrac{100}{95} \times 100=105.3\%$

Say True or False.
The measure of an obtuse angle $< 90^o$.

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

False
The measure of an obtuse angle is greater than $90^o$ but less than $180^o$.

An angle whose measure is the sum of the measures of two right angles is _______.

maths construction of angles identifying angles acute and obtuse angles types of angle

  1. Acute

  2. Obtuse

  3. Right

  4. Straight

Show answer
Correct Option: D
Explanation:

Measure of a right angle is $90^ \circ$

Measure of a straight angle is $180^ \circ$
Sum of the measure of two right angles is $(90+90)^ \circ=180^ \circ$
Thus an angle whose measure is the sum of two right angles is $Straight$