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Finding percentage of a number - class-VII

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$120\%$ of $45$

  1. $45$

  2. $54$

  3. $34$

  4. $43$


Correct Option: B
Explanation:
Given,

$120\%$ of $45$

$=\dfrac{120}{100} \times 45$

$=\dfrac{12}{2} \times 9$

$=6 \times 9$

$=54$

Two-third of one-seventh of a number is $87.5$% of $240$. What is the number?

  1. $2670$

  2. $2450$

  3. $2205$

  4. $1470$


Correct Option: C
Explanation:

Given, $\dfrac {2}{3}$ of $\dfrac {1}{7}$ of a number say $x$ is $87.5\%$ of $240$.

$\therefore \displaystyle \frac{2}{3}\times\frac{1}{7}\times x=\frac{87.5}{100}\times240$

$\displaystyle \Rightarrow x =\frac{87.5\times240\times3\times7}{2\times100}=2205$
therefore, the number is $2205$.

John estimated that the repairs to his car would cost $200$ rupees. In fact they cost $350$ rupees. What was the percentage error?

  1. $52.85\%$

  2. $42.85\%$

  3. $32.85\%$

  4. $22.85\%$


Correct Option: B
Explanation:

Given that: Expected repair of car= $200$
Actual cost of repair = $ 350$
Percentage of error: $\dfrac{Absolute \ value - exact \ value}{Exact \ value} \times 100$
$= \dfrac{350 - 200}{350} \times{100}$

$= 42.85 $ %

You expected to get $50$ gifts for your birthday, but you only got $32$. What was the percentage error?

  1. $51.25\%$

  2. $45.25\%$

  3. $46.25\%$

  4. $56.25\%$


Correct Option: D
Explanation:

Given, absolute value $=50$, exact value $=32$
Percentage error $=$ $\left | \dfrac{Absolute \space\ value - exact \space\ value}{exact\space\ value} \right |\times 100$ $\%$
$=$ $\left | \dfrac{50 - 32}{32} \right |\times 100$ $\%$
$=$ $\left | \dfrac{ 18}{32} \right |\times 100$ $\%$
$=$ $\left | 0.5625\right |\times 100$ $\%$
$= 56.25\%$

10% of 60 + 60% of 100 =?

  1. 90

  2. 46

  3. 66

  4. 70


Correct Option: C
Explanation:

$\dfrac{10}{100}\times60$ + $\dfrac{60}{100}\times100$ $=6+60=66$

After allowing $15$% discount, the selling price of a radio becomes $Rs. 255$. The marked price is

  1. $Rs. 500$

  2. $Rs. 600$

  3. $Rs. 400$

  4. $Rs. 300$


Correct Option: D
Explanation:

Let the marked price of Radio be $Rs. x$.
According to the question, $0.85x = 255$
$x = Rs. 300$
Hence, the marked price of Radio is $Rs. 300$.

Choose the correct answer from the alternatives given.
Some money was lent on $4\%$ compound interest. If the difference in interest of second and the first year is $88$, find out the sum.

  1. $Rs. 50,000$

  2. $Rs. 60,000$

  3. $Rs. 65,000$

  4. $Rs. 55,000$


Correct Option: D

Choose the correct answer from the alternatives given.
Directions for question 71 to 75: Study the following table carefully and answer the questions given below.
Number of Students Enrolled
With Five Colleges over the Years

Year/College A B C D E
2004 450 320 400 480 520
2005 480 350 380 500 540
2006 420 300 410 520 460
2007 460 360 430 470 480
2008 470 340 390 530 530

What is the average number of students enrolled in the college A over the years? 

  1. $456$

  2. $460$

  3. $464$

  4. $452$


Correct Option: A
Explanation:

Total number of students in college over the years$=420+480+420+460+470=2280$

Average no. of students$=2280/5=456$

$60 \% \text { of } 264$ is the same as-

  1. $10 \% \text { of } 44$

  2. $15 \% \text { of } 1056$

  3. $30 \% \text { of } 132$

  4. $17 \% \text { of } 544$


Correct Option: B
Explanation:

$60\% \ of \ 264 =\dfrac{60}{100} \times 264 =158.4$


Also, $15\% \ of \ 1056 =\dfrac{15}{100} \times 1056 = 158.4$

Hence, $60\% \ of \ 264 = 15\% \ of \ 1056$

$0.15 \% \text { of } 33 \frac { 1 } { 3 } \% \text { of } \mathrm { Rs } .10,000$ is?

  1. $\mathrm { Rs } .0 .05$

  2. $\mathrm { Rs } .5$

  3. $\mathrm { Rs } .105$

  4. $\mathrm { Rs } .150$


Correct Option: B
Explanation:

Given 


$0.15\% \times 33\dfrac 13\% \times 10000$

$\implies \dfrac {15}{100}\times \dfrac 1{100}\times \dfrac {100}3 \times \dfrac 1{100}\times 10000$

$\implies \dfrac {15}3=5$

$45 \% \text { of } 1500 + 35 \% \text { of } 1700 = ? \% \text { of } 3175$

  1. 30

  2. 35

  3. 40

  4. 50


Correct Option: C
Explanation:

$45\%$ of $1500$ is given as 

$\dfrac{45}{100}\times 1500$

$\implies 45\times 15=675$

$35\%$ of $1700$ is given as 

$\dfrac {35}{100}\times 1700$

$\implies 35\times 15=595$

Total is $675+595=1270$

Let the percent be $x$ 

$\implies \dfrac x{100}\times 3175=1270$

$\implies x=\dfrac {1270}{3175}\times 100$

$\implies x=40\%$ 

To get $55\%$ of a number, the number should be multiplied by 

  1. $\dfrac {11}{20}$

  2. $3.5$

  3. $\dfrac {7}{50}$

  4. $0.035$


Correct Option: A

Evaluate approximate value of $15.2$% of $726\times 12.8$% of $643.$

  1. $9562$

  2. $9324$

  3. $9082$

  4. $9710$


Correct Option: C
Explanation:

the approximate value of $15.2\%$ of $726 \times 12.8\%$ of $643=$ 

$\dfrac{15.2}{100}\times 726\times \dfrac{12.8}{100}\times 643$
$=9082\cdot 411$
$=9082$ (approx)

In an examination in which full marks were $800$. $A$ gets $20\%$ more than $B$, $B$ gets $20\%$ more than $C$ and $C$ gets $15\%$ less than $D$. If $A$ got $576$, what percentage of full marks did $D$ get? ( approximately)?

  1. $45.7$

  2. $51.2$

  3. $58.8$

  4. $61.7$


Correct Option: C
Explanation:

Given, $\displaystyle A=\frac{120}{100}B$,

$B=\dfrac{120}{100}C$ and 
$C=\dfrac{85}{100}D$
$\Rightarrow B=\dfrac{5}{6}A,C=\dfrac{5}{6}B,D=\dfrac{20}{17}C$
$\displaystyle \Rightarrow  B=\frac{5}{6}\times 576=480$
$\Rightarrow C=\dfrac{5}{6}\times 480=400$
$\Rightarrow D=\dfrac{20}{17}\times 400=\dfrac{8000}{17}$
So, required percentage $\displaystyle =\left ( \frac{8000}{17}\times \frac{1}{800}\times 100 \right )\%=58.82\%$

15 litres of a mixture contain 20% milk and the rest water. If 3 litres of water be mixed in it, the percentage of milk in the new mixture will be ..............

  1. 17%

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

  3. 18$\frac{1}{2}$%

  4. 15%


Correct Option: B
Explanation:

15 litres of a mixture contain 20% milk
So, milk=15*20/100=3 litres
water=15-3=12 litres
3 litres of water is mixed, so 
 new 18 litres of mixture has 15 litres of water and 3 litres of milk
So, percentage of milk= quantity of milk*100/total mixture
$M$ %$=3*100/18$
$=100/6=16\frac { 2 }{ 3 }$ %
Answer (B) 
16$\frac{2}{3}$%


Due to an increase of 30% in the price of eggs. 3  eggs are available for rs. 7.80. The present rate of eggs per dozen is ____.

  1. Rs. 8.64

  2. Rs. 8.88

  3. Rs. 9.36

  4. Rs.10.40


Correct Option: C
Explanation:

Given cost of 3 eggs are Rs 7.80 then cost of one dozen eggs are
=$7.80\times \frac{12}{3}=31.20$Rs
When cost increase 30% Then cost increase on one dozen eggs are=$\times \frac{31.20\times30}{100}=9.36$

What percentage of a day is six hours and 45 minutes?

  1. 7.218%

  2. 8.3%

  3. 28.125%

  4. None of these


Correct Option: C
Explanation:

A day is 24hrs.
 six hours and 45 minutes=
$6\frac { 45 }{ 60 } =6\frac { 3 }{ 4 } =\frac { 27 }{ 4 } Hrs$
So, % of a day=
$=\frac { 27 }{ 4*24 } \times 100$
$=\frac { 27 }{ 4*24 } \times 100=28.13%$
Answer (C) 28.125%

Which is the greatest ?

  1. $\dfrac{50}{3}\%$

  2. $\dfrac{2}{15}$

  3. $0.17$

  4. $6\%$


Correct Option: C
Explanation:

Option A$\Rightarrow \begin{pmatrix}\dfrac{50}{3}\end{pmatrix}\times\begin{pmatrix}\dfrac{1}{100}\end{pmatrix}=\dfrac{1}{6}=0.166$
Option B $\Rightarrow \dfrac{2}{15}=0.133$
Option C $\Rightarrow 6\%=\dfrac{6}{100}=0.06$
Clearly $\Rightarrow 0.17$ is greater

Mary expected to $120$ people for her wedding, but only $60$ people appeared. What was the percentage error?

  1. $75\%$

  2. $25\%$

  3. $55\%$

  4. $100\%$


Correct Option: D
Explanation:

To Calculate percentage error:
Expected number of people = $120$
Actual number of people attended = $ 60$

Percentage of error
=$\dfrac{Absolute value - exact value}{Exact value} \times 100$

 = $ \dfrac{120 - 60}{60} \times{100}$

= $ 100 $ %

Tom expected to $100$ people for his marriage party, but only $80$ people appeared. What was the percentage error?

  1. $75\%$

  2. $25\%$

  3. $55\%$

  4. $65\%$


Correct Option: B
Explanation:

Given, Absolute value $=100$, exact value $=80$

We know, percentage error $=$ $\left | \dfrac{Absolute \space\ value - exact \space\ value}{exact\space\ value} \right |\times 100$%
$=$ $\left | \dfrac{100 - 80}{80} \right |\times 100$%
$=$ $\left | \dfrac{ 20}{80} \right |\times 100$%
$=$ $\left | 0.25\right |\times 100$%
$= 25\%$

What is the percentage approximate for the fraction $\dfrac{12}{35}$?

  1. $34.28\%$

  2. $23.78\%$

  3. $30.12\%$

  4. $29.10\%$


Correct Option: A
Explanation:

To get the percent you will divide the numerator by the denominator.

Then multiply $100$ to the answer and add the percent sign.
therefore, the percentage approximate value if $\dfrac{12}{35}\times 100 = 34.28$ $\%$.

Which of the following statement/formulae is correct for Percentage Error?

  1. $\cfrac { \left| Approx.value-Exact\quad value \right| }{ Exact\quad value } $

  2. $\cfrac { \left| Exact\quad value-Approx.value \right| }{ Exact\quad value } $

  3. $\cfrac { \left| Approx.value-Exact\quad value \right| }{ Approx.value } \quad $

  4. None


Correct Option: A
Explanation:

The approximate values is the estimated values and the exact value is the real value.

In the half yearly exam only $70\%$ of the students were passed. Out of these(assed in half yearly) only $60\%$ students are passed in annual exam. Out of those who did not pass the half yearly exam, $80\%$ passed in annual exam. What per cent of the students passed the annual exam?

  1. $42\%$

  2. $56\%$

  3. $66\%$

  4. $38\%$


Correct Option: C
Explanation:

Let the total students are $100$

Given : $70\%$ students passed in half yearly examination 
Then, passed students in half yearly $=\dfrac{70}{100}\times 100=70$
Out of these passed in half yearly, $60\%$ students passed in yearly 
Then, passed students in yearly examination $=\dfrac{60}{100}\times 70=42$
The no. of students not passed in half yearly examination $=100-70=30$
Given out of these who did not pass the half yearly examination, $80\%$ students passed in annual exam
Then, out of these student who did not pass in half yearly examination, no. of students passed in yearly $=\dfrac{80}{100}\times 30=24$
Then, total no. of students passed annual examination $=42+24=66$
Then, $\%$ of passed students $=\dfrac{66}{100}\times 100=66\%$

I thought 70 people would turn up to the concert, but in fact 80 did. Find the error.

  1. $21.5 \%$

  2. $12.5 \%$

  3. $13.5 \%$

  4. None of these


Correct Option: B
Explanation:

$\dfrac{|Approximate Value - Exact Value|}{|Exact Value|} \times100$


$\dfrac{|70-80|}{80} \times 100$ = $\dfrac{10}{80} \times 100$

$\dfrac{100}{8}$ = $12.5$

Sam does an experiment to find how long it takes an apple to drop $2$ meters. Sam measures $0.62$ seconds, which is an approximate value. Calculate the error percentage.

  1. $4\%$

  2. $3\%$

  3. $6\%$

  4. None of the above


Correct Option: B
Explanation:

we know that ,
$s=\dfrac{at^2}{2}$
$a=g=9.81 msec^{-2}$
$2=\dfrac{9.81t^2}{2}$
$t=\sqrt{\dfrac{4}{9.81}}$
$t=0.6385$
Therefore, error is $(0.6385-0.62)\times 100%=3%$
$3%$ is the error percentage.

I estimated $260$ people, but $325$ came. Find the error as a percent of the exact value.

  1. $20\%$

  2. $40\%$

  3. $30\%$

  4. None of these


Correct Option: A
Explanation:

$\Rightarrow$  Expected people to come is $260$ and actual people came is $325$

$\Rightarrow$  Approximate value is $260$ and exact value is $325$
$\Rightarrow$  $Error=Exact\, value-Approximate\, value =325-260=65$.

$\Rightarrow$  $Percent\,\,error=\dfrac{65}{325}\times 100=20\%$

The report said the carpark held $240$ cars, but we counted only $ 200$ parking spaces. By what percent the report had error?

  1. $10 \%$

  2. $25 \%$

  3. $20 \%$

  4. None of these


Correct Option: C
Explanation:

$\Rightarrow$  Here, Approximate value is $240$

$\Rightarrow$  Exact value is $200$.
$\Rightarrow$  $Percent\, error$ = $\dfrac{|Approximate\,value-Exact\,value|}{Exact\,value}\times 100$

$\Rightarrow$  $Percent\,error=\dfrac{|240-200|}{|200|}\times 100=\dfrac{40}{200}\times 100=20\%$

You measure the plant to be $80$ cm high (to the nearest cm). If you could be up to $0.5$ cm wrong. Calculate your percentage error.

  1. $0.425\%$

  2. $0.525\%$

  3. $0.625\%$

  4. None of these


Correct Option: C
Explanation:

$\Rightarrow$   Measure of plant is $80\,cm$.

$\Rightarrow$   Error is $0.5\,cm$.
$\Rightarrow$  $\%\,Error=\dfrac{0.5}{80}\times 100$
$\therefore$    $\%\,Error=0.625\%$

What is the percentage error in using $\dfrac{22}{7}$ as an approximation for $\pi$?
(Give your answer to the nearest $0.01%$)

  1. $0.02\%$

  2. $0.03\%$

  3. $0.04\%$

  4. None of these


Correct Option: C
Explanation:

$\Rightarrow$  Here, Approximate value of $\pi$ = $\dfrac{22}{7}=3.142857$

$\Rightarrow$  Exact value of $\pi$ is $3.141592$
$\Rightarrow$  $\%\,Error=\dfrac{|Approximate\,value-Exact\,value|}{|Exact\,value|}\times 100$

$\Rightarrow$  $\%\,Error=\dfrac{|3.142857-3.141592|}{|3.141592|}\times 100$
$\Rightarrow$  $\%\,Error=0.04\%$

The population in $2002$ was $29,000$. It was expected to rise to $34,000$ by $2012$. In fact it rose to $33,000$. What was the percentage error?

  1. $25\%$

  2. $15\%$

  3. $12.5\%$

  4. None of these


Correct Option: A
Explanation:

$\Rightarrow$  Here, Approximate Population = $34000-29000=5000$

$\Rightarrow$  Exact population = $33000-29000=4000$
$\Rightarrow$  $\%\,Error=\dfrac{|Approximate\,value-Exact\,value|}{|Exact\,value|}\times 100$

$\Rightarrow$  $\%\,Error=\dfrac{|5000-4000|}{|4000|}\times 100$

$\therefore$   $\%\,Error=25\%$

They forecast 20 mm of rain, but we really got 25 mm. Find the error in percentage.

  1. $-20\%$

  2. $-10\%$

  3. $10\%$

  4. None of these


Correct Option: A
Explanation:

$\dfrac{Approximate Value - Exact Value}{Exact \  Value} \times100$
$\dfrac{20-25}{25} \times 100$ = $\dfrac{-5}{25} \times 100$
$\dfrac{-100}{5}$ = $-20$
Percentage of error $ = - 20\%$.

By evaluating $\dfrac{2.8^3\times 1.2^2}{0.56+3.78}$, closest estimate answer is:

  1. $7$

  2. $70$

  3. $0.7$

  4. None of these


Correct Option: A
Explanation:

We need to evaluate $\dfrac{2.8^3 \times 1.2^2}{0.56+3.78}$

$\Rightarrow$  $\dfrac{3^3 \times 1.44}{4.34}$    $[\because\,\, 2.8\approx 3]$
$\Rightarrow$  $\dfrac{27\times 1}{4}$     $[\because\,\, 1.44\approx 1\,\text{and}\,\,4.34\approx 4]$
$\Rightarrow$  $6.75\approx 7.$
Therefore, $\dfrac{2.8^3\times 1.2^2}{0.56+3.78}=7$

Pankaj expected to earn $425 in a week. In fact he earned $500. What was the percentage error?

  1. $25\%$

  2. $15\%$

  3. $11.5\%$

  4. None of these


Correct Option: B
Explanation:

$\Rightarrow$  Here, Approximate value is $\$425$.

$\Rightarrow$  Exact value is $\$500$.
$\Rightarrow$  $\%\,Error=\dfrac{|Approximate\,value-Exact\,value|}{|Exact\,value|}\times 100$

$\Rightarrow$  $\%\,Error=\dfrac{|425-500|}{|500|}\times 100$

$\Rightarrow$  $\%\,Error=\dfrac{|-75|}{500}\times 100=15\%$

I estimated that the repairs to my car would cost $80. In fact they cost $120. What was the percentage error?

  1. $33.3 \%$

  2. $30.3 \%$

  3. $31.3 \%$

  4. None of these


Correct Option: A
Explanation:

$\dfrac{Approximate Value - Exact Value}{Exact \  Value} \times100$


$\dfrac{80-120}{120} \times 100$ = $\dfrac{40}{120} \times 100$'

$\dfrac{100}{3}$ = $33.3$


Percentage of error $ = 33.3\%$.

Ritika expected to get $50 for her birthday, but she only got $35. What was the percentage error?

  1. $45.9\%$

  2. $32.8\%$

  3. $42.9\%$

  4. None of these


Correct Option: C
Explanation:

$\dfrac{Approximate Value - Exact Value}{Exact Value} \times100$


$\dfrac{50-35}{35} \times 100$ = $\dfrac{15}{35} \times 100$
$\dfrac{1500}{35}$ = $42.9$
percentage of error $42.9$.

Susan tries to read 50 pages of her book every day.  One week (7 days) she only managed to read 280 pages. What was the percentage error?

  1. $25\%$

  2. $15\%$

  3. $2.5\%$

  4. None of these


Correct Option: A
Explanation:

$\Rightarrow$  Here, Approximate value of pages for one week = $50\times 7=350$

$\Rightarrow$  Exact value is $280$
$\Rightarrow$  $\%\,Error=\dfrac{|Approximate\,value-Exact\,value|}{|Exact\,value|}\times 100$

$\Rightarrow$  $\%\,Error=\dfrac{|350-280|}{280}\times 100$

$\Rightarrow$  $\%\,Error=\dfrac{70}{280}\times 100=25\%$

What is the percent error in using $3.14$ as an approximation for $\pi$ (which is $3.14159265358979323846$...) ?

  1. $0.5\%$

  2. $0.05\%$

  3. $0.005\%$

  4. None of these


Correct Option: B
Explanation:

$\Rightarrow$   Here Approximate value of $\pi$ is $3.14$.

$\Rightarrow$   Exact value of $\pi$ is $3.141592$

$\Rightarrow$   $\%\,Error=\dfrac{|Approximate\,valu-Exact\,value|}{|Exact\,value|}\times 100$

$\Rightarrow$  $\%\,Error=\dfrac{|3.14-3.141592|}{|3.141592|}\times 100$
$\Rightarrow$   $\%Error=0.05\%$

Estimated value of square root of $650$ is

  1. $25.495$

  2. $24.495$

  3. $2.5495$

  4. None of these


Correct Option: A
Explanation:

$\Rightarrow$   Here we have to find square root of $650$

$\Rightarrow$  $\sqrt{650}=\sqrt{25\times 26}$
$\Rightarrow$  $\sqrt{650}=5\sqrt{26}$
$\Rightarrow$  $\sqrt{650}=5\times  5.09$
$\Rightarrow$  $\sqrt{650}=25.495$

Round off value of $78.25$m to nearest $10 $m is

  1. $77$ m

  2. $78$ m

  3. $80$ m

  4. None of these


Correct Option: B
Explanation:

Given value is $78.25$

It lies between $78$ and $79.$

But $78.25 < 78.5$ i.e. $78.25$ is closer to $78$ than $79.$

$\therefore  78.25$ should be rounded off to $78m.$

In an examination where full marks were $1000$, A gets $20\%$ more than B, B gets $20\%$ more than C, and C gets $15\%$ less than D. If A got $400$, what percentage of full marks did D get approximately ?

  1. $30\%$

  2. $35\%$

  3. $40\%$

  4. $45\%$


Correct Option: B
Explanation:

Full marks$=1000$

Let assume D got $x\%$ marks

 according to the question
 $C=85\%\times x=0.85x$
 $B=120\%\times 0.85x=1.02x$
 $A=120\%\times 1.02x=1.224x$
Now $A=400$

$1.224x=400$
$\implies x=327$
$\therefore$ percent of $D=(327/1000)\times 100=32.7\%\approx35\%$

Two numbers are less than a third number by $30\%$ and $37\%$ respectively. How much percent is the second number less than the first?

  1. $10\%$

  2. $15\%$

  3. $20\%$

  4. $25\%$


Correct Option: A
Explanation:

Let the $3rd$ number be $100$. Then,


$1st$ number $= 70$ and $2nd$ number $= 63$

$2nd$ number is less than 1st by $(\dfrac{7}{70}\times 100)=10 \%$

Choose the correct answer from the alternative given. 
A man had $100$ kgs of sugar, part of which he sold at $7\%$ profit and rest at $17\%$ profit. He gained $10\%$ on the whole. How much did he sell at $7\%$ profit?

  1. $65$kg

  2. $35$kg

  3. $30$kg

  4. $70$kg


Correct Option: D

$83.33\% $ of coins out of $36$ coins are $20$ paise coins and rest are $10$ paise coins which amounts to $6.60$. Find the number of $10$ paise coins.

  1. $8$

  2. $5$

  3. $6$

  4. $2$


Correct Option: C
Explanation:

Given : $83.33$% of $36$ coins are $20$ paisa coins

$83.33$% of $36 =\left( \cfrac { 83.33 }{ 100 }  \right) \times 36=30$

So, $30$ coins are $20$ paise coins and remaining $(36-30)= 6$ coins are $10$ paise coins.

Value $=30\times 20+6\times 10=660$ Paise $=Rs. 6.60$, which is the given amount.

$\therefore $ Number of $10$ paise coins are $6$.

Choose the correct answer from the alternatives given.
The average age of eleven cricket players is 20 years. If the age of the coach is also included, the average age increases by 10%. The age of the coach is

  1. 48 year

  2. 44 year

  3. 40 year

  4. 36 year


Correct Option: B
Explanation:

Average of 11 players $= 20$ years.
Sum of age of 11 players $= 20 \times 11 = 220$
Average age of players and coach $1.1 \times 20 22$ years
Sum of ages of players & coach $= 22 \times 12 = 264$ years.
Age of coach $= 264 - 220 = 44$ years. 

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