Two candidates appeared for an examination. The marks obtained by one candidate exceeded those of the other by 75. Moreover, his score was equivalent to 80% of the combined marks of both candidates. Determine the marks obtained by each candidate.
Show answer & explanation
Correct answer: D
Explanation
Given:
One candidate's marks are 75 higher than the other's.
His score = 80% of the total marks of both candidates.
According to the formula:
Let the marks of the candidate with the lower score be = x
The marks of the other candidate = x + 75
Total marks = x + (x + 75) = 2x + 75
According to the condition:
x + 75 = 80/100 (2x + 75)
x + 75 = 0.8(2x + 75)
x + 75 = 1.6x + 60
75 − 60 = 1.6x − x
15 = 0.6x
x = 25
Marks of the other candidate = 25 + 75 = 100
25 marks, 100 marks