You can think of "twice cheaper" as meaning "twice the amount for the same price", so "60 times cheaper" means you can buy 60 books for the price of 1.
While that has a logic to it, I don't think that's the logic or meaning of the terms as they are generally used in English. If you mean 98% cheaper, say that, not 60 times cheaper. Two times or three times the price means you multiply it by that integer value. For "less" or "cheaper" people use percentages or fractions. Using an integer for cheaper is wrong, IMO.
While I accept this may not be common usage in English, I am quite certain no one would take "60 times cheaper" to mean "you would literally be paid 60 times the price to take one item". That interpretation makes no sense at all (except if doing some real mental gymnastics to translate common words mechancially into math and then execute the math).
Stil, the phrase itself is just not silly and wrong. It's only uncommon.
The reason it's not silly/wrong is that you can say, and people often do, that something is "much cheaper" than something else, and that clearly means that it is less expensive. So, the language already accepts that a thing becomes less expensive as it becomes cheaper.
So, if it becomes twice as cheap, it becomes half as expensive. Similarly, as something becomes less cheap, it becomes more expensive, so you can also say that something is half as cheap as something else, so it's twice as expensive. There is no ambiguity, it's just an uncommon way of quantifying price changes. Without the speicifc quantifier, the relative comparisons are actually quite common - it would be cheaper to buy X; is not as expensive as Y - common phrases.
