Question

A boy get 25 marks out of 80 and fails by 15 marks. Find the percentage of passing marks.
1. \[40\% \]
2. \[30\% \]
3. \[33\% \]
4. \[50\% \]

Answer 1

Hint: Percentage- It is a number or ratio that can be expressed as a fraction of 100, which means, a part per hundred.
The word per "cent" means per 100.
It is represented by the symbol
1. Percentage formula \[ = \left( {Value/Total{\text{ }}value} \right) \times 100\]
Like, 3 apples out of 15 are rotten then.
Percentage of rotten apples \[ = \left( {3/15} \right) \times 100 = 20\% \]
2. Every percentage problem has three variables.
1. Percentage
2. Part
3. Base
Like, \[25\% \] of 50 is 12.5
Here 25 is percentage
50 is base
12.5 is part
Formula of getting passing percentage passing percentage
\[ = \left( {obtained{\text{ }}marks/total{\text{ }}marks} \right) \times 100\]

Complete step by step answer:
It is given that ,
Marks obtained by boy $ = $ 25
Marks by which he failed $ = $ 15
Maximum marks $ = $ 80
As the boy failed by 15 marks, passing marks should be,
Marks obtained by boy +Marks by which he failed
So, Passing marks \[ = 25 + 15 = 40\]
Percentage of passing marks, $ = $ Passing marks $ \times $ 100
Maximum marks \[ = \dfrac{{40}}{{80}} \times 100\]
\[ = 50\% \]
So, percentage of passing \[ = 50\% \]
Therefore, option D \[ = 50\% \] is the correct option.

Note:
Here are some points to remember-
1. \[p\% \,of{\text{ }}q = q{\text{ }}\% {\text{ }}of{\text{ }}p\]
Like \[100\% {\text{ }}of{\text{ }}60 = \left( {100/100} \right) \times 60 = 60\]
And \[60\% {\text{ }}of{\text{ }}100 = \left( {{\text{ }}60/100} \right) \times 100 = 60\]
2. Percentage change \[ = \left[ {\left( {change{\text{ }}in{\text{ }}value} \right)/\left( {initial{\text{ }}value} \right)} \right] \times 100\]
Like-
A book went from 100Rs to 200Rs, what is the percentage change ?
For this, we will use the above formula.
Percentage change \[ = \left[ {\left( {change{\text{ }}in{\text{ }}value} \right)/\left( {initial{\text{ }}value} \right)} \right] \times 100\]
Percentage change in price \[ = \left[ {\left( {200 - 100} \right)/100} \right] \times 100\]
\[ = \left( {100/100} \right) \times 100\]
\[ = 100\% \]
It means price is increased by \[100\% \]. Which means new price is double of its initial value.