Explanation:

- The batsman's average for the first 16 innings is 36.

- Total runs for the first 16 innings: \(16 \times 36 = 576\).

- In the next innings, he scores 70 runs.

- Total runs after 17 innings: \(576 + 70 = 646\).

- New average after 17 innings: \(\frac{646}{17} = 38\).

- Option 1, 53: This would be possible with incorrectly calculated totals or innings.

- Option 2, 35: This would be less than the original average, which is not logical after a high score.

- Option 3, 106: This would be implausibly high without significantly more runs.

- Option 4, 38: Correct calculation with all factors considered.

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