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Question
Rose got 30% of the maximum marks in an examination and failed by 10 marks. However, Lily who appeared for the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?
Solution
Let maximum marks be x
Rose scored 30% of maximum marks
i.e. Rose scored `30/100` x
Rose failed by 10 marks
∴ passing marks = `30/100 "x" + 10` .....(i)
Lily scored 40% of the maximum marks
i.e. Lily scored `40/100` x
Lily scored 15 marks more than passing marks
∴ passing marks = `(40"x")/100 - 15` ...(ii)
equating (i) and (ii),
`(30"x")/100 + 10 = (40"x")/100 - 15`
∴ 10 + 15 = `(40"x" - 30"x")/100`
∴ 10x = (25)(100)
x = 250
From (i), passing marks = `30/100(250) + 10`
= 75 + 10 = 85
∴ Passing marks for the examination were 85.
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