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A shop ordered 8 dozen type-A pens along with some dozens of type-B pens. Type-A costs 2.5 times as much per dozen as type-B. When delivered, the two quantities were interchanged, raising the bill by 50%. What was the original ratio of type-A to type-B?

1. 1 : 1
2. 4 : 11
3. 2 : 13
4. 13 : 12

Correct answer: 4 : 11

Solution

With B priced 1 and A priced 2.5, original bill = 20 + x and swapped bill = 2.5x + 8. Setting 2.5x+8 = 1.5(20+x) gives x = 22, so 8 : 22 = 4 : 11.

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