What is the meaning of "Pat came the reply"

I was reading following text from a blog post and I experienced difficulty understanding the phrase - "Pat came the reply". I've searched enough (limited to internet search engine) but I didn't find the standard or proper meaning (Suppose, I guess) of this phrase - Pat came the reply.

Emperor Bahadur Shah Zafar asked him:

"Mirza, kitne rozey rakhkhey?" ("Mirza, how many days did you fast?")

Pat came the reply: "Bas huzoor, ek nahin rakhkha" ("Sir, I did not fast for one day")

I've also found the use of the same phrase in a book authored by noted Indian author and journalist Khushwant Singh - K. Singh Best Indian Short Stories-Vol.II.

'No, bothersome. One can't spit.'

Pat came the reply from Namu: 'Right under the chair. Maaro pichkri!'

IMHO, this pat could mean "in a pat manner". From the Merriam-Webster dictionary:

pat: in a pat manner : aptly, perfectly
'She has her part down pat'

To paraphrase,

Mirza replied aptly: "Bas huzoor, ek nahin rakhkha" ("Sir, I did not fast for one day")

Mirza came up with a pat reply: "Bas huzoor, ek nahin rakhkha" ("Sir, I did not fast for one day")

Alternatively, it could be an onomatopoeic "pat". It's as if the reply fell with a sound that could be reproduced as "pat!" Compare: "plop!"; "bam!"; "cling!"; "clang!", etc.

I favor the first version: I googled for "came the reply", and found sentences where the word preceding "came the reply" is clearly an adjective, not an onomatopoeic word:

Speaking about the lessons he learnt from the event in Bangkok, prompt came the reply, "I learnt never to be overconfident at any point." (Deccan Chronicle)

P.S.

From the grammar standpoint, the word pat in your sentences could be analyzed as an adverb. Alternatively, it could be analyzed as an adjective that is part of a secondary predicate. That's my guess. I could be wrong. I'm not sure on this count.

It helps if you're familiar with the expression pat answer. According to TFD, a pat answer is one that is quick, easy, simplified, or evasive. NOAD defines it as simple and somewhat glib or unconvincing.

So, while it could mean the answer was apt and perfectly timed (as others have suggested), it could just as well mean the answer was simple, and didn't provide a lot of extra information.

Either way, pat came the reply is a very unusual way to phrase it. Normally, I think you'd find something like: He gave a pat reply: "Sir, I did not fast for one day."

It may be worth noting that "I did not fast for one day" could be interpreted in two ways: