This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
a) Calculate the amount of money Cherop received more than Asha at the end of the first year. Step 1: Determine the initial contributions and their ratio. Asha's contribution: Ksh 60,000 Nangila's contribution: Ksh 85,000 Cherop's contribution: Ksh 105,000 Total contribution: 60,000 + 85,000 + 105,000 = Ksh 250,000 Ratio of contributions (Asha : Nangila : Cherop): 60,000 : 85,000 : 105,000 Divide by 1,000: 60 : 85 : 105 Divide by 5: 12 : 17 : 21 Total ratio parts: 12 + 17 + 21 = 50 Step 2: Calculate the profit available for sharing. Gross profit for the first year: Ksh 225,000 Amount put back into business (25% of gross profit): 0.25 × 225,000 = Ksh 56,250 Remaining profit: 225,000 - 56,250 = Ksh 168,750 Amount for taxes and insurance (40% of remaining profit): 0.40 × 168,750 = Ksh 67,500 Profit available for sharing among partners: 168,750 - 67,500 = Ksh 101,250 Step 3: Calculate Asha's and Cherop's shares. Asha's share: (12)/(50) × 101,250 = 12 × 2,025 = Ksh 24,300 Cherop's share: (21)/(50) × 101,250 = 21 × 2,025 = Ksh 42,525 Step 4: Calculate the difference. Amount Cherop received more than Asha: 42,525 - 24,300 = Ksh 18,225 Cherop received Ksh 18,225 more than Asha. b) Nangila further invested Ksh 25,000 into the business at the beginning of the second year. Given that the gross profit at the end of the second year increased in the ratio 10:9, calculate Nangila's shares of the profit at the end of the second year. Step 1: Determine the new contributions and their ratio for the second year. Asha's contribution: Ksh 60,000 Nangila's new contribution: 85,000 + 25,000 = Ksh 110,000 Cherop's contribution: Ksh 105,000 Total new contribution: 60,000 + 110,000 + 105,000 = Ksh 275,000 New ratio of contributions (Asha : Nangila : Cherop): 60,000 : 110,000 : 105,000 Divide by 1,000: 60 : 110 : 105 Divide by 5: 12 : 22 : 21 Total new ratio parts: 12 + 22 + 21 = 55 Step 2: Calculate the gross profit for the second year. Gross profit for the first year: Ksh 225,000 Gross profit for the second year increased in the ratio 10:9. Gross Profit (2nd year) = (10)/(9) × 225,000 = 10 × 25,000 = Ksh 250,000 Step 3: Calculate the profit available for sharing in the second year. Amount put back into business (25% of gross profit): 0.25 × 250,000 = Ksh 62,500 Remaining profit: 250,000 - 62,500 = Ksh 187,500 Amount for taxes and insurance (40% of remaining profit): 0.40 × 187,500 = Ksh 75,000 Profit available for sharing among partners: 187,500 - 75,000 = Ksh 112,500 Step 4: Calculate Nangila's share of the profit. Nangila's share: (22)/(55) × 112,500 = (2)/(5) × 112,500 = 2 × 22,500 = Ksh 45,000 Nangila's share of the profit at the end of the second year is Ksh 45,000. Last free one today — make it count tomorrow, or type /upgrade for unlimited.