Word Problem 3
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
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,
Eq (1) and (2) both are expressing pass marks , so both should be equal!
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;
Now eq (1) and (4) both express passing marks, so should be equal!
Subtracting eq(3) and (5) from both sides;
So, total marks were 400
Put this value of x in eq (3) or (5) {we putting in eq 3}
So, passing marks were 40%