Profitable company

Three businessman decide to open up their own company. They agree to distribute the yearly profits made in the same ratio as their initial investments. They invest R 50 000, R 75 000 and R25 000, respectively. The profit made by the company in the first year is R600 000.

(1) Express the ratio of the initial investments in simplest form.
(2) How much will each businessman receive by way of profit?

Result

r = (Correct answer is: 2/3:1) Wrong answer
p1 =  200000
p2 =  300000
p3 =  100000

Solution:

a=50000 b=75000 c=25000  50000=24⋅55 75000=23⋅3⋅55 25000=23⋅55 GCD(50000,75000,25000)=23⋅55=25000  k=GCD(a,b,c)=GCD(50000,75000,25000)=25000  a0=a/k=50000/25000=2 b0=b/k=75000/25000=3 c0=c/k=25000/25000=1  r=2:3:1a=50000 \ \\ b=75000 \ \\ c=25000 \ \\ \ \\ 50000=2^4 \cdot 5^5 \ \\ 75000=2^3 \cdot 3 \cdot 5^5 \ \\ 25000=2^3 \cdot 5^5 \ \\ \text{GCD}(50000, 75000, 25000)=2^3 \cdot 5^5=25000 \ \\ \ \\ k=GCD(a,b,c)=GCD(50000,75000,25000)=25000 \ \\ \ \\ a_{0}=a/k=50000/25000=2 \ \\ b_{0}=b/k=75000/25000=3 \ \\ c_{0}=c/k=25000/25000=1 \ \\ \ \\ r=2:3:1
p=600000 p1=p⋅ 22+3+1=600000⋅ 22+3+1=200000=2.000000⋅105p=600000 \ \\ p_{1}=p \cdot \ \dfrac{ 2 }{ 2+3+1 }=600000 \cdot \ \dfrac{ 2 }{ 2+3+1 }=200000=2.000000\cdot 10^{ 5 }
p2=p⋅ 32+3+1=600000⋅ 32+3+1=300000=3.000000⋅105p_{2}=p \cdot \ \dfrac{ 3 }{ 2+3+1 }=600000 \cdot \ \dfrac{ 3 }{ 2+3+1 }=300000=3.000000\cdot 10^{ 5 }
p3=p⋅ 12+3+1=600000⋅ 12+3+1=100000=1.000000⋅105p_{3}=p \cdot \ \dfrac{ 1 }{ 2+3+1 }=600000 \cdot \ \dfrac{ 1 }{ 2+3+1 }=100000=1.000000\cdot 10^{ 5 }

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