James and Daniel, owners of J.D
chemicals shared their end of the year profit
in the ratio of 4:6. If Daniel (D) got ₦4,000
more than James (J), calculate their total annual profit
Let's say the total end of year profit is P.
The profit ratio between James and Daniel is 4:6, which can also be written as 4x:6x, where x is a common factor.
Since Daniel got ₦4,000 more than James, we can set up the equation:
6x - 4x = ₦4,000
2x = ₦4,000
x = ₦4,000 / 2
x = ₦2,000
Now we can calculate the individual profits:
James' profit (J) = 4x = 4 * ₦2,000 = ₦8,000
Daniel's profit (D) = 6x = 6 * ₦2,000 = ₦12,000
The total annual profit is the sum of their individual profits:
Total profit = J + D = ₦8,000 + ₦12,000 = ₦20,000
Therefore, their total annual profit is ₦20,000.
Let's assume that James' share of the profit is represented by the ratio 4x, where x is the common ratio. Since Daniel got ₦4,000 more than James, Daniel's share of the profit can be represented by 4x + 4000.
According to the given information, the ratio of James' share of the profit to Daniel's share is 4:6. This can be written as:
4x : (4x + 4000) = 4 : 6
To solve this proportion, we can cross multiply:
4(4x + 4000) = 6(4x)
16x + 16000 = 24x
Now, subtract 16x from both sides:
16000 = 8x
Divide both sides by 8:
2000 = x
Now, we can calculate their individual shares:
James (J) = 4x = 4 * 2000 = ₦8,000
Daniel (D) = 4x + 4000 = 4 * 2000 + 4000 = ₦12,000
To calculate their total annual profit, we can add their shares:
Total annual profit = James' share + Daniel's share = ₦8,000 + ₦12,000 = ₦20,000
Therefore, their total annual profit is ₦20,000.