X and Y enter into a partnership with capital in the ratio 3: 5. After 5 months X adds 50% of his capital, while Y withdraws 60% of his capital. What is the share (in ₹ lakhs) of X in the annual profit of ₹ 6.84 lakhs?

Solution

Let X's and Y's initial investment for the first 5 months be 30 and 50 After 5 months, X's capital for next 7 months = (150/100) × 30 = 45 Y's capital for next 7 months = (40/100) × 50 = 20 (X's profit)/(Y's profit) = [(30 × 5) + (45 × 7)]/[(50 × 5) + (20 × 7)] ⇒ (150 + 315)/(250 + 140) ⇒ 465/390 ⇒ 31/26 Total profit = 30 + 26 = 57 units ⇒ (X's profit)/(Total profit) = 31/57 ⇒ (X's profit)/6.84 = 31/57 ⇒ X's profit = (31/57) × 6.84 ⇒ X's profit = 3.72