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)
p₁ =  200000
p₂ =  300000
p₃ =  100000

Step-by-step explanation:

$$\begin{gathered} a=50000 \\ b=75000 \\ c=25000 \\ 50000=2^4\cdot 5^5 \\ 75000=2^3\cdot 3\cdot 5^5 \\ 25000=2^3\cdot 5^5 \\ \text{GCD}(50000,75000,25000)=2^3\cdot 5^5=25000 \\ k=GCD(a,b,c)=GCD(50000,75000,25000)=25000 \\ {a}_0=a\mathrm{/}k=50000\mathrm{/}25000=2 \\ {b}_0=b\mathrm{/}k=75000\mathrm{/}25000=3 \\ {c}_0=c\mathrm{/}k=25000\mathrm{/}25000=1 \\ r=2:3:1 \end{gathered}$$

$$\begin{gathered} p=600000 \\ {p}_1=p\cdot {\displaystyle \frac{2}{2+3+1}}=600000\cdot {\displaystyle \frac{2}{2+3+1}}=200000 \end{gathered}$$

$p_2=p\cdot {\displaystyle \frac{3}{2+3+1}}=600000\cdot {\displaystyle \frac{3}{2+3+1}}=300000$

$p_3=p\cdot {\displaystyle \frac{1}{2+3+1}}=600000\cdot {\displaystyle \frac{1}{2+3+1}}=100000$

Try another example

Related math problems and questions:

• Twelve
  Twelve students work on a week forestry brigade. One hundred spruces will receive x CZK, one hundred pine y CZK. How many receive each one students did in one day if they planted a total of 25,000 spruces per week and 30,000 pine trees? Express by express
• On Children's
  On Children's Day, the organizers bought 252 chewing gums, 396 candies and 108 lollipops. They want to make as many of the same packages as possible. Advise them what to put in each package and how many packages they can make this way.
• Lcm = 22 + gcd
  The least common multiple of two numbers is 22 more than their greatest common divisor. Find these numbers.
• Simplest form 3
  What fraction is 15 of 35 in simplest form?
• Shepherd
  The shepherd has fewer than 500 sheep; where they can be up to 2, 3, 4, 5, 6 row is always 1 remain, and as can be increased up to 7 rows of the sheep, and it is not increased no ovine. How many sheep has a shepherd?
• Quotient
  Find quotient before the bracket - the largest divisor 51 a + 34 b + 68 121y-99z-33
• Reminder and quotient
  There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1.
• Tissues
  The store got three kinds of tissues - 132 children, 156 women and 204 men. Tissues each species were packed into boxes after the number of pieces the same for all three types (and greatest). Determine the number, if you know that every box has more than
• Bricks pyramid
  How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
• Blades
  1st blade 2,5 m, 2nd blade. .1.75 m. How many same long pieces of this two blades can be do the biggest? How long is one piece?
• Ratios
  Reduce the numbers: 50 in a 1:2 ratio 111 at a ratio of 2:3 70 at 10:50 560 at a ratio of 3:8
• A map 3
  A map is drawn to a scale of 1 : 25 000. This scale can be expressed as 1 cm represents n km. Find n.
• Sports students
  There are 120 athletes, 48 volleyball players, and 72 handball players at the school with extended sports training. Is it possible to divide sports students into groups so that the number in each group is the same and expressed by the largest possible num
• Three friends
  Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together.
• Colorado
  The state Colorado has the shape of a rectangle. The map is sold on 2 posters. The first has dimensions of 70 cm and 50 cm in a scale of 1: 1,000,000. The second poster has dimensions of 175 cm and 125 cm. What is the scale of the second poster?
• A number 5
  A number is divisible by 24, 25, and 120 if it is increased by 20. Find the number.
• Cutting paper
  Divide a rectangular paper with dimensions 220mm and 308mm into squares of the same size so that they are as large as possible. Specify the length of the side of the square.