A shop ordered 8 dozen type-A pens and some dozen type-B pens. Type-A costs 2.5 times type-B per dozen. When delivered, quantities swapped, bill increased 50%. Ratio type-A:type-B original?

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Accepted Answer

1. Let price of type-B per dozen be $p$. Then type-A price = $2.5p=\frac{5}{2}p$.

2. Original bill = $8	imes\frac{5}{2}p + x	imes p = (20 + x)p$.

3. After swap bill = $8p + x	imes\frac{5}{2}p = (8 + 2.5x)p$.

4. Swap increases bill by 50%: $8 + 2.5x = 1.5(20 + x)$. So $8 + 2.5x = 30 + 1.5x$, giving $x=22$.

5. Ratio type-A:type-B = $8:22 = 4:11$. **Answer (b).**

FINAL_ANSWER: b

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