Arun ordered 8 kg of type-A sugar and some additional kilograms of type-B sugar. Type-A costs twice as much per kg as type-B. When delivered, quantities were swapped, increasing the bill by 35%. Find the ratio of original type-A to type-B quantity.

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1. Let type-B price be $p$ and type-A price be $2p$. Let type-B qty be $x$.
2. Original bill = $16p + xp$. Delivered bill = $8p + 2xp$.
3. Given $8p+2xp = 1.35(16p+xp)$. Divide by $p$: $8+2x = 1.35(16+x)$. So $0.65x = 13.6$ and $x = 272/13$.
4. Ratio $8 : x = 8 : 272/13 = 104 : 272 = 13 : 34$. **Answer (b).**
FINAL_ANSWER: b

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