The batting average of a cricket player for 64 innings is 62 runs. His highest score exceeds his lowest score by 180 runs. Excluding these two innings, the average of remaining innings becomes 60 runs. His highest score was :

214 runs

The correct answer is Option 1: 214 runs

Total innings = 64
Average = 62 runs

Total runs in 64 innings = 64 × 62 = 3968 runs

Highest score = H
Lowest score = L

Given:
H − L = 180 …(1)

Excluding these two innings:
Remaining innings = 62
New average = 60

Total runs of remaining 62 innings = 62 × 60 = 3720

So, runs scored in highest + lowest innings:

3968 − 3720 = 248
⇒ H + L = 248 …(2)

Now solve equations:

H − L = 180
H + L = 248

Add both:

2H = 428
H = 214