
Shortcut Trick
If the average increases, the score in the new match provides the old average plus the extra runs required to increase the average for all matches.
Total extra runs needed to increase the average of 17 matches by 2.5 = 17 × 2.5 = 42.5 runs.
Old Average = Score in 17th match − Total extra runs
Old Average = 98 − 42.5 = 55.5
∴ The correct answer is 55.5 runs.

Alternate Method
Given:
Runs scored in the 17th match = 98 runs
Increase in average = 2.5 runs
Formula Used:
Average = Total Runs ÷ Number of Matches
Breakdown of 17th Match Score (98 runs)
Old Average (x)
Increase (17 × 2.5)
Total Runs in 17th Match = 98
Calculations:
⇒ Let the average before the 17th match be x.
⇒ Total runs scored in 16 matches = 16x
⇒ Total runs after playing 17 matches = 16x + 98
⇒ New average after the 17th match = x + 2.5
⇒ So, (16x + 98) ÷ 17 = x + 2.5
⇒ 16x + 98 = 17 × (x + 2.5)
⇒ 16x + 98 = 17x + 42.5
⇒ 17x − 16x = 98 − 42.5
⇒ x = 55.5
∴ The correct answer is 55.5 runs.

Additional Information
New Average Formula
When a new value is added to a group: New Value = Old Average + (Total Number of Entities × Increase in Average).
Combined Average
The combined average of two independent groups is given by (N1A1 + N2A2) ÷ (N1 + N2), where N is the number of items and A is the respective average of the groups.
Weighted Average
Used when different values contribute differently to the final average: W.A. = (w1x1 + w2x2 + ... + wnxn) ÷ (w1 + w2 + ... + wn).