Neha and Siya started a partnership with investments of Rs P and Rs (P + 5000), respectively. Neha invested her amount for 3T years, while Siya invested for 2T years. If Neha’s profit share is Rs 18,000 out of the total profit of Rs 42,000, find Siya’s investment.

ATQ, Neha’s investment = Rs P. Siya’s investment = Rs (P + 5000). Neha’s time = 3T years. Siya’s time = 2T years. Total profit = Rs 42,000. Neha’s profit share = Rs 18,000. Siya’s profit share = 42,000 − 18,000 = Rs 24,000. Profit ratio of Neha and Siya = 18000 : 24000 Profit ratio = 3 : 4. In partnership, profit ratio = investment × time. So, P × 3T : (P + 5000) × 2T = 3 : 4. Cancel T from both sides. 3P : 2(P + 5000) = 3 : 4. Cross multiply: 4 × 3P = 3 × 2(P + 5000) 12P = 6(P + 5000) 12P = 6P + 30000 12P − 6P = 30000 6P = 30000 P = 30000/6 P = 5000 Siya’s investment = P + 5000 Siya’s investment = 5000 + 5000 Siya’s investment = Rs 10,000