Stack Life Cycle

#1

Let S be a stack of size n >= 1. Starting with the empty stack, suppose we push the first n natural numbers in sequence, and then perform n pop operations. Assume that Push and Pop operation take X seconds each, and Y seconds elapse between the end of one such stack operation and the start of the next operation. For m >= 1, define the stack-life of m as the time elapsed from the end of Push(m) to the start of the pop operation that removes m from S.
The average stack-life of an element of this stack is

n(X+ Y)

3Y + 2X

n(X + Y)-X

Y + 2X

i am not able to understand how the answer is n(X+Y)-X

#2

https://www.geeksforgeeks.org/gate-gate-cs-2003-question-64/ Here is the solution for it.

#3

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