It was that which made him decide to resign that summer,when he was sixty five.
I could not understand why the writer used both relative pronouns (that,which) together?
It was that which made him decide to resign that summer,when he was sixty five.
I could not understand why the writer used both relative pronouns (that,which) together?
That is not a relative pronoun in this sentence, it is a demonstrative pronoun. It refers to a fact that has just been stated. Let's look at the preceding sentence:
In 1913 Chips had had bronchitis and was off duty for nearly the whole of the winter term. It was that which made him decide to resign that summer, when he was sixty-five.
"That" replaces the whole preceding sentence.
You could rephrase the sentence as:
The fact that he had had bronchitis in 1913 and was off duty for nearly the whole of the winter term made Chips decide to resign that summer.
Which is the only relative pronoun in the sentence you quoted and it refers to that.