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Money and metric measures as percentage - class-VIII

Description: money and metric measures as percentage
Number of Questions: 33
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Tags: percentages fractions and standard forms percentage maths comparing quantities using proportion percentage and simple interest percent and percentage percent comparing quantities
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Which of the following is a non-positive and non-negative integer ?

  1. 1

  2. 0

  3. -1

  4. 3


Correct Option: B
Explanation:

The correct answer is 0 (b)

Since zero is neither positive nor negative .

Ram scored $30$% marks and failed by $15$ marks. Aditya score $40$% marks and obtained $35$ marks more than those required to pass. The pass percentage is?

  1. $33$%

  2. $38$%

  3. $43$%

  4. $46$%


Correct Option: A
Explanation:
Let the total no of marks for $x$
Let the passing marks for y
$\dfrac{30}{100}x+15=y$ ______(1)
$\dfrac{40}{100}x=y+35$
$\dfrac{40}{100}x-35=y$_______(2)
(1) - (2)
$\dfrac{-10x}{100}+50=0$
$\dfrac{10x}{100}=50\Rightarrow x=500$
$y=\dfrac{40}{100}\times 500-35=200-35=165$
$m\%$ of $x=y$
$\dfrac{m}{100}\times 500=165$
$m=33\%$

If $35\% $ of a number is $175$, then what percent of $175$ is that number ?

  1. $35\% $

  2. $65\% $

  3. $285.71\% $

  4. $420\% $


Correct Option: C
Explanation:
Let the required number be $x$

It is given that $35$% of that number is $175$

=> $\dfrac { 35 \times  x }{ 100 } =175$

=> $x= \dfrac { 175 \times  100 }{ 35 }$

=> $x= 500$

Now, the question requires the percentage that $500$ is of that number

Let that percentage be $y \%$.

Now, $\dfrac { y \times  175 }{ 100 } =500$

=>$ y=\dfrac { 500 \times  100 }{ 175 } $

=>$ y = 285.714$

Hence the answer is $ 285.71\%$

$2.7$ is what percent of $18$ ?

  1. $12$%

  2. $13$%

  3. $14$%

  4. $15$%


Correct Option: D
Explanation:

Percentage = $\dfrac {2.7}{18}$ $\times 100$


= $\dfrac {270}{18}$

= $\dfrac {30}{2}$ (removing common factor of 9)


= $15$%

If $2\, \displaystyle \frac{1}{2}\, \%$ofa a number is 0.2, then what will be 120 % of it?

  1. 10.8

  2. 4.8

  3. 9.6

  4. None


Correct Option: C
Explanation:

$2\, \displaystyle \frac{1}{2}\, \%$ of x = 0.2


$\displaystyle \frac{5}{200}\, \times\, x\, =\, 0.2$

$x\, =\, 0.2\, \times\, \displaystyle \frac{200}{5}\, =\, 8$

120 % of $8\, =\, \displaystyle \frac{120}{100}\, \times\, 8\, =\, 9.6$

If 37% of a number is 990.86. What will be approximately 19% of that number?

  1. 600

  2. 500

  3. 700

  4. 550


Correct Option: B
Explanation:

Let the number is x
then $x\times 37\div 100 = 990.80$
$x = 2678 approx$
$ 2678 \times 19 \div 100 = 508 = 500 approx$

If $p _1\%$ of number $N _1$ is equal to $p _2\%$ of number $N _2$, what percent of $N _1$ is $N _2$?

  1. $\displaystyle\frac{100p _1}{p _2}$

  2. $\displaystyle\frac{100p _2}{p _1}$

  3. $\displaystyle\frac{p _1}{p _2}$

  4. $\displaystyle\frac{p _2}{p _1}$


Correct Option: B
Explanation:

$\displaystyle\frac{p _1}{100}\times N _1=\frac{p _2}{100}\times N _2$

$\displaystyle\frac{N _1}{N _2}=\frac{p _2}{p _1}$, $\displaystyle N=\frac{p _2}{p _1}\times N _2$

Percent of $\displaystyle N _1=\left(\frac{p _2}{p _1}\times100\right)\%$ of $N _2$

Percent of $\displaystyle N _2=\left(\frac{p _2}{p _1}\times100\right)\%$ of $N _1$

Successive Comminssion of $20$%, $10$% and $5$% on an atricle is equivalent to the commission

  1. $31$%

  2. $31.6$%

  3. $32.5$^

  4. $35$%


Correct Option: A
Explanation:

Over all discount$=100\%-(80\%\times 90\%\times 95\%)=100\%-68.4\%=31.6\%$

$1000$ is how many times of $10$

  1. $200$

  2. $100$

  3. $300$

  4. $400$


Correct Option: B
Explanation:

$\dfrac { 1000 }{ 10 } =100$

The value of a machine is Rs. $6,250$. It decreases by $10$% during the first year, $20$% during the second year and $30$% during the third year. What will be the value of the machine after $3$ years?

  1. Rs. $2,650$

  2. Rs. $3,050$

  3. Rs. $3,150$

  4. Rs. $3,510$


Correct Option: C
Explanation:
Value after $1^{st}$ year $=6250-\dfrac {10}{100}\times 6250$
$=5625\ Rs$
Value after $2^{nd}$ year $=5625-\dfrac {20}{100}\times 5625=\dfrac {80}{100}\times 5625$
$=4500\ Rs$
Value after $3^{rd}$ year $=4500-\dfrac {30}{100}\times 4500=\dfrac {70}{100}\times 4500$
$=Rs\ 3150$


$88 \% \text { of } 370 + 24 \% \text { of } 210 - x? = 118$

  1. 256

  2. 258

  3. 268

  4. 358


Correct Option: B
Explanation:

$88\% \ of \ 370+24\% \ of \ 210-x=118$

$\dfrac{88}{100}\times 370 +\dfrac{24}{100} \times 210-x=118$

$\dfrac{3256}{10}+\dfrac{504}{10}-x=118$

$325.6+50.4-118=x$
$x=258$

A spider climbed $62\cfrac{1}{2}$% of the height of the pole in one hour and in the next hour it covered $12\cfrac{1}{2}$% of the remaining height. If pole's height is $192m$, then the distance climbed in second hour is:

  1. $3m$

  2. $5m$

  3. $7m$

  4. $9m$


Correct Option: D

In an examination in which full marks were $500$. $A$ got $25$% more than $C$, $C$ got $20$% less than $D$. If $A$ got $360$ marks. What percentage of full marks was obtained by $D$?

  1. $72$%

  2. $80$%

  3. $50$%

  4. $60$%


Correct Option: A
Explanation:
given,full marks in the examination are $500$
A got $360$ marks  
A got $25\%$ more than $C$.
let the marks of $C$ be $'x'$ then, 
$x+\dfrac{25}{100}\times x=360$ 
$\dfrac{5x}{4}=360$
$x=288$
 so,$C$ got $288$ marks . 
given,$C$ got $20\%$ less than $D$ let the marks of $D$ be $'y'$ then,
 $y-\dfrac{20}{100}\times y=288$
 $\dfrac{4y}{5}=288$
$y=360$
 so,$D$ got $360$ marks percentage of full marks obtained by $D$ $=\dfrac{360}{500}\times 100$
$=72\%$

Tulsiram's salary is $20$% more than that of Kashyap. If tulsiram saves RS. $720$ which is $4$% of his salary, then Kashyap's salary is

  1. Rs. $15,000$

  2. Rs. $12,000$

  3. Rs. $10,000$

  4. RS. $22,000$


Correct Option: A
Explanation:

$Salary\quad of\quad Tulsiram$

$ =Rs\quad \dfrac { 720 }{ 4 } \times 100$

$=Rs\quad 18,000$

$Salary\quad of Kashyap\quad $

$=18000\times \dfrac { 100 }{ 120 } $

$ =Rs.15000$

In two successive years, $80$ and $60$ students of a school appeared at the final examination, of which $60$% and $80$% passed respectively. The average rate of students passed (in percent) is:

  1. $68$%

  2. $68\cfrac{4}{7}$%

  3. $32$%

  4. $36$%


Correct Option: B

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

  1. $20$%

  2. $25$%

  3. $30$%

  4. $40$%


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 $x$

$12.5\% \,of\,192 = 50\% \,of\,?$ 

  1. $48$

  2. $96$

  3. $24$

  4. none of these


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 $54$ ?

  1. $81$%

  2. $83$%

  3. $85$%

  4. None of these


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.

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

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

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

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


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.

  1. $25\%$

  2. $22.5\%$

  3. $20\%$

  4. $30\%$


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?

  1. 25%

  2. 24%

  3. 22%

  4. 20%


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 ?

  1. 20%

  2. 16%

  3. 25%

  4. 15%


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

  1. $600$

  2. $800$

  3. $1025$

  4. $1175$


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?

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

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

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

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


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

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


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 

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

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

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

  4. None


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

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

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

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

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


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?

  1. 40%

  2. 50%

  3. 60%

  4. 70%


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

  1. $490$

  2. $500$

  3. $1960$

  4. $1800$


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 $12$?

  1. $133.33$%

  2. $100$%

  3. $120$%

  4. $150$%


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 _________.

  1. $5$

  2. $15$

  3. $24$

  4. $60$


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 $25\%$?

  1. $6.25$

  2. $0.625$

  3. $0.0625$

  4. $0.00625$


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 $q$?

  1. 105%

  2. 105.3%

  3. 110%

  4. 115%


Correct Option: B
Explanation:

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

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

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