Word Problem 3

Percentage Comparison 0

Problem 3: In an examination a candidate who secures 25% of the maximum marks fails by 60 marks. Another candidate who secures 42 % of the total marks gets 8 marks more than necessary for passing. Find the maximum marks and the percentage for passing.

(word problems on job exam mathematics.)

Solution:

Let the maximum marks =’x’

And let there be two candidates ‘A’ and ‘B’

Let pass marks = y% of x

$Pass Marks = \frac{y}{100}x$

$Pass Marks = \frac{yx}{100}----(1)$

We consider ‘A’s case

Candidate ‘A’

‘A’ gets 25% marks of total marks and fails by 60 marks. It means had had’A’ got 60 more marks he would has passed the exam ! i-e 25%+60 marks would have made him successful.

so we say mathematically,

$Total Marks = x$

$A Got Marks =\frac{25}{100} x$

$To Make Him Pass He Needed =\frac{25}{100} x+60----(2)$

Eq (1) and (2) both are expressing pass marks , so both should be equal!

$\Rightarrow \frac{25}{100} x+60= \frac{yx}{100}$

$\Rightarrow \frac{25}{100} x+60= \frac{yx}{100}-----(3)$

Now we consider ‘B’s case

Candidate ‘B’

“B’ gets 42% marks of total marks ‘x’ which are 8 marks more than needed to pass, i-e if 8 marks were deducted from his score than remaining marks would be equal to passing marks!

We write mathematically;

$Total Marks = x$

$'B' Got Marks = \frac{42}{100}x$