Tag: maths

Questions Related to maths

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

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

  1. $25\%$

  2. $15\%$

  3. $11.5\%$

  4. None of these

Show answer
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?

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

  1. $33.3 \%$

  2. $30.3 \%$

  3. $31.3 \%$

  4. None of these

Show answer
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?

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

  1. $45.9\%$

  2. $32.8\%$

  3. $42.9\%$

  4. None of these

Show answer
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?

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

  1. $25\%$

  2. $15\%$

  3. $2.5\%$

  4. None of these

Show answer
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 $3.14159265358979323846$...) ?

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

  1. $0.5\%$

  2. $0.05\%$

  3. $0.005\%$

  4. None of these

Show answer
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

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

  1. $25.495$

  2. $24.495$

  3. $2.5495$

  4. None of these

Show answer
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

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

  1. $77$ m

  2. $78$ m

  3. $80$ m

  4. None of these

Show answer
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 ?

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

  1. $30\%$

  2. $35\%$

  3. $40\%$

  4. $45\%$

Show answer
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?

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

  1. $10\%$

  2. $15\%$

  3. $20\%$

  4. $25\%$

Show answer
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?

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

  1. $65$kg

  2. $35$kg

  3. $30$kg

  4. $70$kg

Show answer
Correct Option: D