1. **Problem 55:** Arvind, Bhavin, and Chandan invest in a business at different times and amounts. Total profit is 105000. Find Chandan's share. 2. **Formula:** Profit share is proportional to the product of investment and time invested. 3. **Calculate investment-time products:** - Arvind: 80000 × 12 = 960000 - Bhavin: 120000 × 8 = 960000 - Chandan: 160000 × 4 = 640000 4. **Total investment-time:** 960000 + 960000 + 640000 = 2560000 5. **Chandan's share:** $$\frac{640000}{2560000} \times 105000 = 26250$$ --- 6. **Problem 56:** A invests 80000 for 9 months, B invests 120000 for 6 months. Total profit is 45000. Find B's share. 7. **Calculate investment-time products:** - A: 80000 × 9 = 720000 - B: 120000 × 6 = 720000 8. **Total investment-time:** 720000 + 720000 = 1440000 9. **B's share:** $$\frac{720000}{1440000} \times 45000 = 22500$$ --- 10. **Problem 57:** Find average of integers between 100 and 250 divisible by 11. 11. **Find first and last multiples:** - First multiple ≥ 100: 11 × 10 = 110 - Last multiple ≤ 250: 11 × 22 = 242 12. **Number of terms:** $$22 - 10 + 1 = 13$$ 13. **Average:** $$\frac{110 + 242}{2} = 176$$ --- 14. **Additional calculations:** - Total proficient in Python = 50 + 70 = 120 - Total proficient in Java = 50 + 60 = 110 - Ratio Python:Java = $$\frac{120}{110} = \frac{12}{11}$$