Find the Distance between Aplha and Gamma

Answer: Distance between Alpha and Gamma is 90 km


Explanation
Maharshi walks from Alpha to Gamma in 4 days.
Let us assume he walks x km in first day
(x-1) km in second day
(x-2) km in third day
(x-3) km in fourth day

Let total distance between Alpha and Gamma be d.
d = x + (x-1) + (x-2) + (x-3)
d = 4x - 6

Now, Gamma to Alpha which which Maharshi finishes in 5 days.

(x-4) km in first day
(x-5) km in second day
(x-6) km in third day
(x-7) km in fourth day
(x-8) km in fifth day

Total distance between Gamma and Alpha
d = (x-4) + (x-5) + (x-6) + (x-7) + (x-8)
so d = 5x - 30


As distance between Aplha and Gamma is same as distance between Gamma and Alpha
4x - 6 = 5x - 30
x = 24

Substituting the value of x in equation d = 4x - 6

d = 4(24) - 6
d = 90 km