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Sanjeni and Mkinwa entered into a business partnership in which they contributed ksh. 120,000 and sh. 150,000 every year, respectively. After one year, Kuku joined the business and contributed sh. 90,000.

Mathematics

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2 parts
a
4 : 5 : 2
b

47,600 Ksh47,600 \text{ Ksh}

59,500 Ksh59,500 \text{ Ksh}

23,800 Ksh23,800 \text{ Ksh}

Step-by-step solution

7 steps

Huu hapa ni ufumbuzi wa swali la 25:

Part a· 4 steps

Ili kukokotoa uwiano wa uwekezaji wao baada ya miaka 3 ya biashara, tunahitaji kuhesabu jumla ya uwekezaji wa kila mtu kwa kipindi chote.

  1. Kokotoa jumla ya uwekezaji wa Sanjeni.

    Sanjeni aliwekeza Ksh. 120,000 mwanzoni kwa miaka 3.

    Uwekezaji wa Sanjeni=120,000×3=360,000 Ksh\text{Uwekezaji wa Sanjeni} = 120,000 \times 3 = 360,000 \text{ Ksh}
  2. Kokotoa jumla ya uwekezaji wa Mkinwa.

    Mkinwa aliwekeza Ksh. 150,000 kila mwaka kwa miaka 3.

    Uwekezaji wa Mkinwa=150,000×3=450,000 Ksh\text{Uwekezaji wa Mkinwa} = 150,000 \times 3 = 450,000 \text{ Ksh}
  3. Kokotoa jumla ya uwekezaji wa Kuku.

    Kuku alijiunga baada ya mwaka mmoja na kuchangia Ksh. 90,000. Hii inamaanisha Kuku aliwekeza kwa miaka 3−1=23 - 1 = 2.

    Uwekezaji wa Kuku=90,000×2=180,000 Ksh\text{Uwekezaji wa Kuku} = 90,000 \times 2 = 180,000 \text{ Ksh}
  4. Andika uwiano wa uwekezaji wao na kurahisisha.

    Uwiano wa uwekezaji = Sanjeni : Mkinwa : Kuku

    360,000:450,000:180,000360,000 : 450,000 : 180,000

    Gawanya kila namba kwa 10,000:

    36:45:1836 : 45 : 18

    Gawanya kila namba kwa 9 (kigawanyo kikubwa zaidi):

    369:459:189\frac{36}{9} : \frac{45}{9} : \frac{18}{9} 4:5:24 : 5 : 2

    Uwiano wa uwekezaji wao ni 4:5:2\boxed{4 : 5 : 2}.

Part b

47,600 Ksh47,600 \text{ Ksh}

Ili kukokotoa sehemu ya faida ya kila mtu, kwanza tunahitaji kupata faida inayobaki baada ya gharama za uendeshaji.

  1. Kokotoa faida inayobaki baada ya gharama za uendeshaji.

    Faida yote ilikuwa Ksh. 187,000.
    30% ya faida ilitumika kwa gharama za uendeshaji.
    Faida inayobaki = 100%−30%=70%100\% - 30\% = 70\% ya faida yote.

    Faida inayobaki=0.70×187,000 Ksh\text{Faida inayobaki} = 0.70 \times 187,000 \text{ Ksh} Faida inayobaki=130,900 Ksh\text{Faida inayobaki} = 130,900 \text{ Ksh}
  2. Gawanya faida inayobaki kulingana na uwiano wa uwekezaji.

    Uwiano wa uwekezaji ni 4:5:24 : 5 : 2.
    Jumla ya sehemu za uwiano = 4+5+2=114 + 5 + 2 = 11.

  3. Kokotoa sehemu ya faida ya kila mtu.

    Sehemu ya Sanjeni:

    411×130,900 Ksh=4×11,900 Ksh=47,600 Ksh\frac{4}{11} \times 130,900 \text{ Ksh} = 4 \times 11,900 \text{ Ksh} = 47,600 \text{ Ksh}

    Sehemu ya Mkinwa:

    511×130,900 Ksh=5×11,900 Ksh=59,500 Ksh\frac{5}{11} \times 130,900 \text{ Ksh} = 5 \times 11,900 \text{ Ksh} = 59,500 \text{ Ksh}

    Sehemu ya Kuku:

    211×130,900 Ksh=2×11,900 Ksh=23,800 Ksh\frac{2}{11} \times 130,900 \text{ Ksh} = 2 \times 11,900 \text{ Ksh} = 23,800 \text{ Ksh}

    Sehemu ya faida ya kila mtu ni:
    Sanjeni: 47,600 Ksh\boxed{47,600 \text{ Ksh}}
    Mkinwa: 59,500 Ksh\boxed{59,500 \text{ Ksh}}
    Kuku: 23,800 Ksh\boxed{23,800 \text{ Ksh}}

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