In a triangular shaped bus station, there is space for 279 buses in the first row, 277 in the second, 275 in the third and so on. There is space for 5 buses in the last row. How many rows are there in the bus station?

The first row has 279 buses, and the second row has 277 buses, the third row has 275 buses...and so on

This forms a decreasing A.P with a common difference of 2

The first term of A.P, a = 279, common difference = -2 and last term $$a_n$$ = 5

We know, in an AP $$a_n=a+\left(n-1\right)d$$

=> 5 = 279 + (n-1)*(-2)

=> (n-1)*2 = 274

=> n-1 = 137

Therefore, n = 138

A total of 138 rows are there in the bus station.

The answer is option A.