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Question
In a debate competition, the judges decide that 20 per cent of the total marks would be given for accent and presentation. 60 per cent of the rest are reserved for the subject matter and the rest are for rebuttal. If this means 8 marks for rebuttal, then find the total marks.
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Solution
Let x be the total marks.
Marks given for accent and presentation = 20% of x
= `20/100 xx x`
= `x/5`
Remaining marks = `x - x/5 = (4x)/5`
Marks reserved for subject matter = 60% of rest marks
= `60/100 xx (4x)/5`
= `(12x)/25`
Now, remaining marks
= `(4x)/5 - (12x)/25`
= `(20x- 12x)/25`
= `(8x)/25`
According to the question,
∴ `(8x)/25 = 8`
⇒ `x = (8 xx 25)/8 = 25`
Hence, total marks are 25.
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