A starts a business with ₹75,000 and B joins the business 5 months later with an investment of ₹80,000. After 1 year, they earn a profit of ₹4,08,800. Find the share of A and B (in ₹).

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**Solution:**

1. Calculate the capital-time product for A and B:
   - A invests ₹75,000 for 12 months: $75,000 	imes 12 = 9,00,000$
   - B invests ₹80,000 for 7 months (since B joins 5 months later): $80,000 	imes 7 = 5,60,000$

2. Find the ratio of their capital-time contributions:
   $$A : B = 9,00,000 : 5,60,000 = 90 : 56 = 45 : 28$$

3. Total profit is ₹4,08,800. Divide it in the ratio 45:28:
   - Sum of ratio parts = $45 + 28 = 73$
   - A's share = $\frac{45}{73} 	imes 4,08,800 = 2,52,000$
   - B's share = $\frac{28}{73} 	imes 4,08,800 = 1,56,800$

**Answer:** ₹2,52,000 and ₹1,56,800

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