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Math  /  Algebra

Question8. Two business partners Nzau and Masese contributed sh. 112,000 and sh 128,000 respectively, to start a business. They agree to share their profits as follows; 30%30 \% to be shared equally 30%30 \% to be shared in the ratio of their contributions 40%40 \% to be retained for the running of the business. If their total profit for the year 1989 was sh. 86400 calculate i) The amount received by each partner ii) The amount retained for running the business

Studdy Solution

STEP 1

1. Nzau and Masese contributed sh. 112,000 and sh. 128,000 respectively.
2. The total profit for the year 1989 was sh. 86,400.
3. 30% of the profit is shared equally between the partners.
4. 30% of the profit is shared in the ratio of their contributions.
5. 40% of the profit is retained for the running of the business.
6. We need to calculate the amount received by each partner and the amount retained for running the business.

STEP 2

1. Calculate the total amount of profit to be shared equally.
2. Calculate the total amount of profit to be shared in the ratio of their contributions.
3. Calculate the amount retained for running the business.
4. Calculate the total amount received by each partner.

STEP 3

Calculate the total amount of profit to be shared equally.
Equally shared profit=0.30×86,400 \text{Equally shared profit} = 0.30 \times 86,400
Equally shared profit=25,920 \text{Equally shared profit} = 25,920

STEP 4

Calculate the total amount of profit to be shared in the ratio of their contributions.
Ratio shared profit=0.30×86,400 \text{Ratio shared profit} = 0.30 \times 86,400
Ratio shared profit=25,920 \text{Ratio shared profit} = 25,920

STEP 5

Calculate the amount retained for running the business.
Retained profit=0.40×86,400 \text{Retained profit} = 0.40 \times 86,400
Retained profit=34,560 \text{Retained profit} = 34,560

STEP 6

Calculate the total amount received by each partner.
First, calculate the amount each partner receives from the equally shared profit:
Equally shared profit for each=25,9202 \text{Equally shared profit for each} = \frac{25,920}{2}
Equally shared profit for each=12,960 \text{Equally shared profit for each} = 12,960
Next, calculate the ratio of their contributions:
Nzau’s contribution ratio=112,000112,000+128,000=112,000240,000=715 \text{Nzau's contribution ratio} = \frac{112,000}{112,000 + 128,000} = \frac{112,000}{240,000} = \frac{7}{15}
Masese’s contribution ratio=128,000112,000+128,000=128,000240,000=815 \text{Masese's contribution ratio} = \frac{128,000}{112,000 + 128,000} = \frac{128,000}{240,000} = \frac{8}{15}
Now calculate the amount each partner receives from the ratio shared profit:
Nzau’s ratio profit=715×25,920 \text{Nzau's ratio profit} = \frac{7}{15} \times 25,920
Nzau’s ratio profit=12,096 \text{Nzau's ratio profit} = 12,096
Masese’s ratio profit=815×25,920 \text{Masese's ratio profit} = \frac{8}{15} \times 25,920
Masese’s ratio profit=13,824 \text{Masese's ratio profit} = 13,824
Finally, calculate the total amount received by each partner:
Nzau’s total=12,960+12,096 \text{Nzau's total} = 12,960 + 12,096
Nzau’s total=25,056 \text{Nzau's total} = 25,056
Masese’s total=12,960+13,824 \text{Masese's total} = 12,960 + 13,824
Masese’s total=26,784 \text{Masese's total} = 26,784
The amount received by Nzau is sh. 25,056, the amount received by Masese is sh. 26,784, and the amount retained for running the business is sh. 34,560.

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