Challenging circular question (Empty bobbin) An almost empty bobbin is pulled along a flat surface by a thread which is wrapped around it. The diameter of the inner reel is 5cm and that of the outer wheels is 10 cm. Assuming no slipping or sliding, how far, in centimeters, has the bobbin moved when the end of the thread has moved 12cm? I got the answer of 24cm. But the correct answer is 8am. Can anyone try to solve it? Thanks in advance.

When the bobbin rolls one complete turn to the right, it has travelled $10\pi$ cm. So the center of the inner reel has also travelled that distance. The amount of thread in one turn around the inner reel is $5 \pi$ cm. So assuming that the thread is coming off the top of the inner reel, the end of the thread has moved $10 \pi$ cm + $5 \pi$ cm = $15 \pi$ cm. So: for $10\pi$ cm of movement of the bobbin, we get $15 \pi$ cm of movement of the thread-end. That's a ratio of 3 to 2.

When the thread has moved 12cm, the bobbin must have moved $8$cm.

**Note:** it's also possible for the thread to come off the _bottom_ of the bobbin, and in this case, $10\pi cm$ movement of the bobbin causes only $10 \pi - 5\pi$ = $5 \pi$ cm movement of the thread, i.e., a ratio of 1 to 2. So that when the thread has moved $12cm$, the bobbin must have moved $24$cm (i.e., your answer).

The question is fundamentally ambiguous.