Ratio and proportion

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?

Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms?

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?

Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?

When a mixture of gases burn, will the volume change?