1. **Problem statement:** A batsman has an average of 37 runs after 17 innings. We want to find how many runs he should score in the next innings so that his average increases by 6 runs. 2. **Given:** - Current average $= 37$ - Number of innings $= 17$ - Increase in average $= 6$ 3. **Formula for average:** $$\text{Average} = \frac{\text{Total runs}}{\text{Number of innings}}$$ 4. **Calculate total runs after 17 innings:** $$\text{Total runs} = 37 \times 17 = 629$$ 5. **New average after next innings:** $$37 + 6 = 43$$ 6. **Let the runs scored in the next innings be $x$. Then total runs after 18 innings:** $$629 + x$$ 7. **Using the new average formula:** $$43 = \frac{629 + x}{18}$$ 8. **Multiply both sides by 18:** $$43 \times 18 = 629 + x$$ 9. **Calculate left side:** $$774 = 629 + x$$ 10. **Solve for $x$:** $$x = 774 - 629 = 145$$ 11. **Answer:** The batsman should score **145 runs** in the next innings to increase his average by 6 runs.