Three brothers in a business deal share the profit at the end of a contract. The first received 1/3 of the…

Analysis

To solve this problem, we need to determine the total profit by tracking the fractions given to each brother and equating the final remaining amount to the total.

Concept

We represent the total profit as $x$. We will subtract the portions taken by the first and second brothers from the whole ($1$) to find the fraction that represents the third brother's share.

Step-by-Step Solution

1. Define the total profit: Let the total profit be $x$.

2. Calculate the first brother's share: The first brother receives $\frac{1}{3}x$. The remainder after the first brother is: $1 - \frac{1}{3} = \frac{2}{3}x$

3. Calculate the second brother's share: The second brother receives $\frac{2}{3}$ of the remainder. Share = $\frac{2}{3} \times (\frac{2}{3}x) = \frac{4}{9}x$

4. Calculate the third brother's share: The third brother receives what is left after the first and second brothers have taken their shares. Total taken by first and second = $\frac{1}{3}x + \frac{4}{9}x$ To add these, find a common denominator (9): $\frac{3}{9}x + \frac{4}{9}x = \frac{7}{9}x$

The third brother's share is the remainder: $1 - \frac{7}{9} = \frac{2}{9}x$

5. Solve for $x$: We are told the third brother's share is N12,000. $\frac{2}{9}x = 12,000$ Multiply both sides by 9: $2x = 108,000$ Divide by 2: $x = 54,000$

Conclusion

The total profit shared by the three brothers is N54,000.00.

Exam Tip: When a question mentions "of the remainder," always calculate the remaining fraction first before multiplying by the next fraction. A common mistake is to multiply the second fraction by the original total instead of the remainder.