Calculate the profit available for sharing among partners for the first year.

Step 1: Calculate the profit available for sharing among partners for the first year. The total profit for the first year is Ksh 4,800,000. First, 25% of the profit is put back into the business: Amount for business = 0.25 × 4,800,000 = Ksh 1,200,000 The remaining profit is: Remaining profit = 4,800,000 - 1,200,000 = Ksh 3,600,000 Next, 20% of the remaining profit is set aside for taxes and insurance: Amount for taxes/insurance = 0.20 × 3,600,000 = Ksh 720,000 The profit available for sharing among partners is: Profit for sharing = 3,600,000 - 720,000 = Ksh 2,880,000 Step 2: Calculate Tanui's investment (x) for part (a)(i). The partners' contributions are Eliza: Ksh 90,000, Nekesa: Ksh 130,000, and Tanui: Ksh x. The total contribution is 90,000 + 130,000 + x = 220,000 + x. Tanui's share of the profit is Ksh 960,000. The profit is shared in the ratio of their contributions. Tanui's shareProfit for sharing = Tanui's contributionTotal contribution (960,000)/(2,880,000) = (x)/(220,000 + x) Simplify the fraction on the left: (1)/(3) = (x)/(220,000 + x) Cross-multiply to solve for x: 220,000 + x = 3x 220,000 = 2x x = (220,000)/(2) x = Ksh 110,000 a) (i) Tanui invested Ksh 110,000. Step 3: Find the ratio of contributions for part (a)(ii). The contributions are Eliza: Ksh 90,000, Nekesa: Ksh 130,000, and Tanui: Ksh 110,000. The ratio is: Eliza : Nekesa : Tanui = 90,000 : 130,000 : 110,000 Divide each number by 10,000 to simplify the ratio: 9 : 13 : 11 a) (ii) The ratio of contributions by the three partners is 9:13:11. Step 4: Calculate the new contributions and new gross profit for the second year for part (b). Nekesa invested an additional Ksh 30,000. New contributions: • Eliza: Ksh 90,000 • Nekesa: 130,000 + 30,000 = Ksh 160,000 • Tanui: Ksh 110,000 New total contribution: 90,000 + 160,000 + 110,000 = Ksh 360,000 The gross profit increased in the ratio 6:5. New gross profit = (6)/(5) × 4,800,000 = 6 × 960,000 = Ksh 5,760,000 Step 5: Calculate the profit available for sharing for the second year. First, 25% of the new gross profit is put back into the business: Amount for business = 0.25 × 5,760,000 = Ksh 1,440,000 The remaining profit is: Remaining profit = 5,760,000 - 1,440,000 = Ksh 4,320,000 Next, 20% of the remaining profit is set aside for taxes and insurance: Amount for taxes/insurance = 0.20 × 4,320,000 = Ksh 864,000 The profit available for sharing among partners is: Profit for sharing = 4,320,000 - 864,000 = Ksh 3,456,000 Step 6: Calculate Nekesa's share of the profit at the end of the second year. Nekesa's contribution is Ksh 160,000. The total contribution is Ksh 360,000. Nekesa's share = Nekesa's contributionTotal contribution × Profit for sharing Nekesa's share = (160,000)/(360,000) × 3,456,000 Simplify the fraction (160,000)/(360,000) = (16)/(36) = (4)/(9): Nekesa's share = (4)/(9) × 3,456,000 Nekesa's share = 4 × 384,000 Nekesa's share = Ksh 1,536,000 b) Nekesa's share of the profit at the end of the second year is Ksh 1,536,000. 3 done, 2 left today. You're making progress.