For example, can I say
Recently I bought a new computer, the price of which was very reasonable.
I always considered this type of usage correct but can’t find any example sentences on the internet.
If you are asking whether the construction
N N Prep. which
is a legal construction in English, then then answer is yes. If your question is whether such a construction is always the best stylistic choice, then the answer is “it depends.”
Beginning in the late 18th century and continuing throughout the next, prescriptivist grammarians argued that as whose was the possessive case of who, its antecedent must be animate. Further, since interrogative whose always references a person — if you ask “Whose key is this?” you get the name of a person, not a house or car — then its usage should be consistent.
Both in terms of etymology and usage, this was utter nonsense, but there were still those who insisted on this rule, even when more observant scholars in the 20th c. pointed out its absurdity.
If the relative clause is nonrestrictive, of which instead of whose is a perfectly acceptable choice:
Andrew Sheets of Morgan Stanley suggests an index of junk-rated property bonds, the price of which may not rise much further in a growing economy but would fall fast in a shrinking one. — The Economist
In this sentence, the price itself is more topical than the fact that it’s the price of the bonds, so of which conveys that topicality while whose would do so somewhat less.
In a restrictive clause, however, it jams two nouns together whose grammatical relationship is not immediately apparent, causing the sentence to lack flow:
If it is determined that the domestic cheese the price of which is claimed to be undercut is not similar to the quota cheese allegedly undercutting it, there shall be no finding of price-undercutting. — The Code of Federal Regulations of the United States of America, 1979.
As you can see, the 18th century casts a long shadow. Stylistically, however, domestic cheese whose price is the better, more natural choice because it sets the condition whereby there will be no determination of undercutting much more smoothly and unambiguously. For instance, in the following sentence
Awning stripes in soft shades of cream and gray are painted onto the walls of a guest room at designer Catherine Memmi’s getaway in Normandy, France, a house whose color scheme references the moody landscape. — Elle Decor, 10 May 2010.
a house the color scheme of which references the moody landscape would completely ruin the flow.
The only way the construction is possible with other prepositions is, barring an intervening prepositional phrase, when the second noun is a nonrestrictive appositive of the first.
Anaximenes is usually viewed as the inventor of Material Monism, the theory by which there is only one substance (in this case air) of which all other stuffs are mere modifications or states … — Daniel W. Graham, The Texts of Early Greek Philosophy, 2010.
Born in a small town in the present-day Czech Republic, Freud grew up in Vienna, the city in which he lived until the last year of his life. — Univ. of Hawaii, CriticaLink.