M and N invested Rs. 3200 and Rs. 4800 respectively. After 15 months, M raised his investment by 25% and N decreased his by Rs. 800. If total profit after 3 years is Rs. 9,600, find the difference in their profit shares.

Total time = 36 months Split into two parts: First 15 months Next 21 months M’s investment: First 15 months: 3200 Next 21 months: 3200 × 1.25 = 4000 N’s investment: First 15 months: 4800 Next 21 months: 4800 − 800 = 4000 M’s capital × time: = (3200 × 15) + (4000 × 21) = 48000 + 84000 = 132000 N’s capital × time: = (4800 × 15) + (4000 × 21) = 72000 + 84000 = 156000 Ratio of profits (M:N) = 132000:156000 = 11:13 Total profit = 9600 M’s share = (11/24) × 9600 = 4400 N’s share = (13/24) × 9600 = 5200 Difference = 5200 − 4400 = ₹800