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A candidate takes a test and attempts all the 100 questions in it. While any correct answer fetches 1 mark, the wrong answers are penalised as follows; one-tenth of the questions carry 1/10 negative marks each, one-fifth of the questions carry 1/5 negative marks each and the rest of the questions carry 1⁄2 a negative mark each. Unattempted questions carry no marks. What is the difference between the maximum and the minimum marks that he can score? 

A candidate takes a test and attempts all the 100 questions in it. While any correct answer fetches 1 mark, the wrong answers are penalised as follows; one-tenth of the questions carry 1/10 negative marks each, one-fifth of the questions carry 1/5 negative marks each and the rest of the questions carry 1⁄2 a negative mark each. Unattempted questions carry no marks. What is the difference between the maximum and the minimum marks that he can score?  Correct Answer 140

GIVEN:

For minimum marks:

one-tenth questions = 1/10 negative mark each

one-fifth questions = 1/5 negative mark each

Rest = 1/2 negative mark each

CONCEPT:

First for maximum marks let's assume he answers all questions correctly.

CALCULATION:

Maximum marks = 100.

so one tenth ,one fifth of 100 questions are 10 and 20 questions respectively.

Negative marks for 30 questions = -(10/10) + (20/5) = -5

70 questions carry = (70 × 1/2) = 35 negative marks.

Total negative marks = (35 + 5) = 40 marks

∴ difference = 100 - (-40) = 140

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