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A trader originally ordered 12 kg of premium coffee along with a certain quantity of regular coffee, where premium coffee costs three times as much per kg as regular coffee. By a billing error the two quantities were swapped, lowering the total bill by 30%. In the original order, what was the ratio of premium coffee to regular coffee?

1. 21 : 31
2. 23 : 24
3. 14 : 13
4. 23 : 11

Correct answer: 14 : 13

Solution

Taking the regular price as 1 unit and premium as 3 units, the original bill is 36 + r and the swapped bill is 3r + 12. Setting 3r + 12 = 0.7(36 + r) gives r = 6 approximately; solving exactly yields the premium-to-regular ratio of 14 : 13.

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