Two warning triangles on different hills show steep-gradient plates: one reads '20%' and the other, an older sign, reads '1 in 8'. Which hill is steeper, and why?
- The hill marked '20%' is steeper, because a percentage gradient equals 100 divided by the ratio's second number, and 20% corresponds to a ratio of 1 in 5, a steeper ratio than 1 in 8
- The hill marked '1 in 8' is steeper, because a smaller written number on an older sign always indicates a steeper gradient than a percentage figure
- The two hills are equally steep, because '20%' and '1 in 8' are simply two different eras of writing exactly the same gradient
- Neither figure indicates steepness on its own; only the supplementary distance plate fitted beneath the sign determines which hill is steeper
Why A? And why not the others?
Correct answer: A. The hill marked '20%' is steeper, because a percentage gradient equals 100 divided by the ratio's second number, and 20% corresponds to a ratio of 1 in 5, a steeper ratio than 1 in 8
UK gradient signs have used a percentage figure since the mid-1970s, with older '1 in N' ratio signs allowed to remain in place until they reach the end of their working life, so the two formats do turn up side by side on the road network. The two scales convert directly: percentage equals 100 divided by the ratio's second number, so a '1 in 8' hill is 100 divided by 8, or 12.5%, rounding to about 13%. A '20%' hill therefore converts to 1 in 5 (100 divided by 20), a noticeably steeper drop over the same horizontal distance than 1 in 8, so the percentage-marked hill in this pair is the steeper one, not the reverse. The claim that a smaller printed ratio number always beats a percentage figure ignores that the two numbers must actually be converted onto the same scale before comparing them; instinctively comparing '20' to '8' without converting is exactly the mistake this sign format catches out. The two figures are not remotely equivalent here, and no distance plate is involved in indicating steepness at all, a distance plate states how long the gradient continues, not how steep it is.
Source: DfT Know Your Traffic Signs — Warning signs (Steep hill gradient signs, GOV.UK); Traffic Signs Manual, Chapter 4: Warning Signs (GOV.UK)