Question

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In an exam 70% student passed in English, 65% passed in maths, 25% failed in both the subject. If 3000 student passed in both subject, then how many students appeared for the exam? ​

Answer 1

$\red{\boxed{\mathfrak\colorbox{pink}{ANSWER}}}$

Let the total no of students be 100x

No of students failed =10*100x /100 = 10x

Thus , no of students passed = 100x - 10x = 90x

No of students passed in english = 7* 100x /100 =70x

No of students passed in maths = 8*100x / 100 =80x

Therefore no of students who passed in both = (80x + 70x) - 90x = 60 x

{{ Draw a venn diagram to understand this point ,

Or you could think like this:- when we add no of students passing in m and e individually ,we are counting those students who passed in both twice ,

Thus total students passed will be sum of no of students passed in maths and english individually - those who passed both.

Rearrange this eqn to get the one used above}}

Thus 60x = 144

Or, 100x = (144 * 100)/60=240

Therefore total no of students = 240

Hope you understood

Answer 2

$\red{\boxed{\mathfrak\colorbox{pink}{ANSWER}}}$

Let the total no of students be 100x

No of students failed =10*100x /100 = 10x

Thus , no of students passed = 100x - 10x = 90x

No of students passed in english = 7* 100x /100 =70x

No of students passed in maths = 8*100x / 100 =80x

Therefore no of students who passed in both = (80x + 70x) - 90x = 60 x

{{ Draw a venn diagram to understand this point ,

Or you could think like this:- when we add no of students passing in m and e individually ,we are counting those students who passed in both twice ,

Thus total students passed will be sum of no of students passed in maths and english individually - those who passed both.

Rearrange this eqn to get the one used above}}

Thus 60x = 144

Or, 100x = (144 * 100)/60=240

Therefore total no of students = 240

Hope you understood