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: $12 + 17 + 21 = 50$

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:

$$168,750 - 67,500 = \text{Ksh } 101,250$$

Asha's share:

$$\frac{12}{50} \times 101,250 = 12 \times 2,025 = \text{Ksh } 24,300$$

Cherop's share:

$$\frac{21}{50} \times 101,250 = 21 \times 2,025 = \text{Ksh } 42,525$$

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.

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: $12 + 22 + 21 = 55$

Gross profit for the first year: Ksh 225,000
Gross profit for the second year increased in the ratio 10:9.

$$\text{Gross Profit (2nd year)} = \frac{10}{9} \times 225,000 = 10 \times 25,000 = \text{Ksh } 250,000$$

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:

$$187,500 - 75,000 = \text{Ksh } 112,500$$

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 $\boxed{\text{Ksh } 45,000}$.