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$\pu{24 kt}$ gold indicates that $24/24$ part of it, i.e. $100\%$ of it is gold. $\pu{18 kt}$ indicates that $18/24$ part of it is gold. As gold is a soft element, I reckoned that $\pu{18 kt}$ gold would be harder than $\pu{24 kt}$ gold.

I recently saw on a website that $\pu{18 kt}$ gold is harder than $\pu{9 kt}$ gold, which surprised and confused me. Now I want to know which karat gold is harder of $\pu{18 kt}$ and $\pu{24 kt}$.

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    $\begingroup$ If you reckon that 18kt gold is harder than 24kt gold, why are you surprised that 9kt gold is harder than 18kt gold? $\endgroup$ – Jon Custer Jun 26 '18 at 15:02
  • $\begingroup$ Addition of any alloy , usually Cu, Ni, Ag, Zn, and others, will harden pure gold by solid solution. And pure gold or any alloy can be hardened by cold work. $\endgroup$ – blacksmith37 Jun 26 '18 at 16:12
  • $\begingroup$ Since the carat scale only tells you about the amount of gold but nothing about what else is in the alloy, it won't directly relate to the hardness (there might even be some alloys softer than gold, though they would be practically useless so probably rare). $\endgroup$ – matt_black Jul 12 '18 at 14:56
  • $\begingroup$ Please do not rollback edits that are for the improvement of your post. If you have any specific concerns, please comment in chat via an @ ping. $\endgroup$ – Gaurang Tandon Jul 24 '18 at 1:36
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18 kt gold is generically harder than 24 kt gold. Both the site you linked and another site agree on that. Pure gold really is quite soft, and when you add things to it, it will get harder.

Now, one key to your problem with understanding the hardness of gold and its alloys is that multiple different alloys can be called "18 kt gold". Different alloys will have different properties and hardness. Interestingly, there is a titanium/gold alloy that is ~4× harder than titanium normally is. The paper - Science Advances 2016, 2 (7), e1600319 - on it looks interesting.

Back to the topic on hand, note in the table below that there are different values for hardness for each carat of gold based on how it has been physically worked and how it has been alloyed. Also note that all the values listed for 18 kt gold are significantly above that of 24 kt gold.

Mechanical Properties of Typical Gold Alloys
Source: Total Materia; Gold and Gold Alloys; Table 3: Mechanical Properties of Typical Gold Alloys

It might be worth a separate question of why 9 kt gold might be listed as softer than 18 kt gold, if it has more in the way of impurities.

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