A firm and Joan entered into a business partnership in which they contributed Ksh. 320000 and Ksh. 400000 every year respectively. After one year, Kevin joined the business and contributed Ksh. 240000. (a) Calculate the ratio of their investment after three years of business.

• Uwekezaji halisi wa Betty = Kiasi cha uwekezaji $\times$ Muda $$320,000 \times 3 \text{ miaka} = \text{Ksh. } 960,000$$
• Uwekezaji halisi wa Joan = Kiasi cha uwekezaji $\times$ Muda $$400,000 \times 3 \text{ miaka} = \text{Ksh. } 1,200,000$$
• Kevin alijiunga baada ya mwaka 1, kwa hivyo aliwekeza kwa $3 - 1 = 2$ miaka. Uwekezaji halisi wa Kevin = Kiasi cha uwekezaji $\times$ Muda $$240,000 \times 2 \text{ miaka} = \text{Ksh. } 480,000$$

Uwiano (Betty : Joan : Kevin) = $960,000 : 1,200,000 : 480,000$
Gawanya kwa 10,000: $96 : 120 : 48$
Gawanya kwa 24: $4 : 5 : 2$
Uwiano wa uwekezaji wao ni $\boxed{4 : 5 : 2}$.

Jumla ya faida = Ksh. 561,000.
Gharama za uendeshaji = 30% ya faida

Faida iliyobaki = Jumla ya faida - Gharama za uendeshaji

5 : 2).
Jumla ya sehemu za uwiano = $4 + 5 + 2 = 11$.

• Sehemu ya Betty = $\frac{4}{11} \times 392,700 = \text{Ksh. } 142,800$
• Sehemu ya Joan = $\frac{5}{11} \times 392,700 = \text{Ksh. } 178,500$
• Sehemu ya Kevin = $\frac{2}{11} \times 392,700 = \text{Ksh. } 71,400$ Kila mtu alipata: Betty $\boxed{\text{Ksh. } 142,800}$, Joan $\boxed{\text{Ksh. } 178,500}$, Kevin $\boxed{\text{Ksh. } 71,400}$.

• Uwekezaji mpya wa Betty = Uwekezaji wa awali wa Betty + Sehemu ya faida ya Betty $$320,000 + 142,800 = \text{Ksh. } 462,800$$
• Uwekezaji mpya wa Joan = Uwekezaji wa awali wa Joan + Sehemu ya faida ya Joan $$400,000 + 178,500 = \text{Ksh. } 578,500$$
• Uwekezaji mpya wa Kevin = Uwekezaji wa awali wa Kevin + Sehemu ya faida ya Kevin $$240,000 + 71,400 = \text{Ksh. } 311,400$$

Uwekezaji wao mpya ni: Betty $\boxed{\text{Ksh. } 462,800}$, Joan $\boxed{\text{Ksh. } 578,500}$, Kevin $\boxed{\text{Ksh. } 311,400}$.