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Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

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
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

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

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

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
Reveal answer Fill a bubble to check yourself
A Correct answer
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\%$.
Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

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
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $42.9$.

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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

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

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

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
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

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

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

Estimated value of square root of $650$ is

  1. $25.495$
  2. $24.495$
  3. $2.5495$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

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. $45\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $D=(327/1000)\times 100=32.7\%\approx35\%$

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

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. $25\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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


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

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

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

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
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the allegation method: the profit percentages are 7 and 17, with a mean of 10. The ratio of quantities is (17-10) : (10-7) = 7 : 3. Total parts = 10, so 7/10 of 100kg = 70kg.