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: $60,000 + 85,000 + 105,000 = \text{Ksh } 250,000$ 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): $$ 0.25 \times 225,000 = \text{Ksh } 56,250 $$ Remaining profit: $$ 225,000 - 56,250 = \text{Ksh } 168,750 $$ Amount for taxes and insurance (40% of remaining profit): $$ 0.40 \times 168,750 = \text{Ksh } 67,500 $$ Profit available for sharing among partners: $$ 168,750 - 67,500 = \text{Ksh } 101,250 $$ Step 3: Calculate Asha's and Cherop's shares. Asha's share: $$ \frac{12}{50} \times 101,250 = 12 \times 2,025 = \text{Ksh } 24,300 $$ Cherop's share: $$ \frac{21}{50} \times 101,250 = 21 \times 2,025 = \text{Ksh } 42,525 $$ Step 4: Calculate the difference. Amount Cherop received more than Asha: $$ 42,525 - 24,300 = \text{Ksh } 18,225 $$ Cherop received $\boxed{\text{Ksh } 18,225}$ 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: $85,000 + 25,000 = \text{Ksh } 110,000$ Cherop's contribution: Ksh 105,000 Total new contribution: $60,000 + 110,000 + 105,000 = \text{Ksh } 275,000$ 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. $$ \text{Gross Profit (2nd year)} = \frac{10}{9} \times 225,000 = 10 \times 25,000 = \text{Ksh } 250,000 $$ Step 3: Calculate the profit available for sharing in the second year. Amount put back into business (25% of gross profit): $$ 0.25 \times 250,000 = \text{Ksh } 62,500 $$ Remaining profit: $$ 250,000 - 62,500 = \text{Ksh } 187,500 $$ Amount for taxes and insurance (40% of remaining profit): $$ 0.40 \times 187,500 = \text{Ksh } 75,000 $$ Profit available for sharing among partners: $$ 187,500 - 75,000 = \text{Ksh } 112,500 $$ Step 4: Calculate Nangila's share of the profit. Nangila's share: $$ \frac{22}{55} \times 112,500 = \frac{2}{5} \times 112,500 = 2 \times 22,500 = \text{Ksh } 45,000 $$ Nangila's share of the profit at the end of the second year is $\boxed{\text{Ksh } 45,000}$. Last free one today — make it count tomorrow, or type /upgrade for unlimited.