Usually when someone does not think your current statement has to do with the conversation at hand they can ask, "What does that have to do with the price of tea in China"?
Where did that form of statement come from?
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Eric Partridge, "A Dictionary of Catch Phrases," says this one is a variant of "What's that got to do with the price of eggs?" and has been around "since the 1940s--perhaps influenced by the expression, e.g. 'I wouldn't do that, not for all the tea in China.'" He identifies the "eggs" saying as "US: since the 1920s, if not earlier."
No one here seems to have actually answered the question in terms of the origin. The phrase is believed to have begun in 19th century England where the actual price of tea in China was of interest. When someone in the British House of Commons said something others felt was irrelevant, it was met with this saying... meaning, the price of tea in China is a relevant topic, but yours is not.
The complete expression is actually the following question: "What does that have to do with the price of tea in China?"
The price of tea in China is completely irrelevant to the subject of conversation. So, when someone asks this question, it means they’re really surprised by the listener's comments. Effectively, they're saying:
The Wikipedia article Irene mentioned is pretty good.
I am going to agree with the "evolution" of a sarcastic answer from a sarcastic answer from a real answer to a real problem: Meaning, originally A LOT of England's money and finance WAS tied up in the price of tea - at the unloading docks in London each year. "Tea races" were highly looked at events covering months of travel and high drama from China around Cape Horn to England to get the first cargo back to London! It affected what everybody drunk and how much everybody bought and paid for their meals and drinks. Very, very important - just like today, the price of oil IS a daily report on the news and in the stock markets.
But, in China, at the China docks? A little bit less important, but relevent. People, companies, industries made their yearly profits - and thus the yearly wages and salaries and earnings for everybody from the owner to the stockholders to the lowest laborer - on how much the difference in price of tea was between the China docks and the London sales rooms. A late ship, a lost ship or spoiled tea product? Disaster. A bad market in China or a bad growing year or famine or a crop failure over there?