A pilgrim starts walking for a journey of 115 km. On the first day he covers 7 km, the next day 9 km, and likewise keeps adding 2 km everyday till he reaches 15 km per day which he maintains for the rest of the journey. How many days in all will he take to complete the journey?

Correct option is C

Given:
Total distance = 115 km. Daily distances form 7, 9, 11, 13, 15, 15, 15, ... (after reaching 15 km/day he continues at 15 km/day).

Formula / Logic Used:

Sum of arithmetic progression for the increasing-days part: S = n × (first + last) / 2.

Remaining distance after that part is covered by equal daily distance (15 km/day) → additional days = remaining / 15.

Solution:
Increasing sequence until 15: 7, 9, 11, 13, 15 → number of terms n = 5.
Sum of these 5 days = 5 × (7 + 15) / 2 = 5 × 22 / 2 = 5 × 11 = 55 km.
Remaining distance = 115 − 55 = 60 km.
Days needed at 15 km/day = 60 / 15 = 4 days.
Total days = 5 + 4 = 9 days.

Correct Answer: (c) 9