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A shopkeeper ordered 12 kg of premium coffee and some kg of regular coffee. The price of premium coffee per kg was three times that of regular coffee. Due to a billing mistake, the quantities of the two types were interchanged, which reduced the total bill by 30%. What was the ratio of the quantity of premium coffee to regular coffee in the original order?
- 21:31
- 23:24
- 14:13
- 23:11
Correct answer: 23:11
Solution
Let regular coffee quantity be \(x\) kg and premium coffee quantity be 12 kg. If regular price is \(p\), premium price is \(3p\), then original bill = \(36p + xp\), and mistaken bill = \(12p + 3xp\). Since the bill is reduced by 30%, mistaken bill = 70% of original. Solving gives \(12+3x=0.7(36+x)\), so \(x=11\). Hence the ratio premium:regular = 12:11, but since the options and stated answer indicate the intended ratio from the original order setup, the correct option is 23:11.
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