Percentages and Applications

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

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

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

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 $Rs. 300$.

For compound interest at rate r, the interest in the first year is Pr and in the second year is Pr*(1+r). The difference is Pr^2. Given r=0.04 and difference=88, we have P(0.04)^2 = 88, so P*0.0016 = 88, which gives P = 55,000.

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

Given 

To find 55 percent of a number, you multiply it by 55/100. Simplifying the fraction 55/100 by dividing both numerator and denominator by 5 gives 11/20.

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

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

15 litres of a mixture contain 20% milk
So, milk=1520/100=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 milk100/total mixture
$M$ %$=3*100/18$
$=100/6=16\frac { 2 }{ 3 }$ %
Answer (B) 16$\frac{2}{3}$%

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=$\times \frac{31.20\times30}{100}=9.36$

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=
$=\frac { 27 }{ 424 } \times 100$
$=\frac { 27 }{ 424 } \times 100=28.13%$
Answer (C) 28.125%

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

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 $ %

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

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

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

Let the total students are $100$

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

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.

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

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

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

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

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

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

$\dfrac{20-25}{25} \times 100$ = $\dfrac{-5}{25} \times 100$

$\dfrac{-100}{5}$ = $-20$
Percentage of error $ = - 20%$.

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

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

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

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

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

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

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

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 $78m.$

Full marks$=1000$

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