Three brothers in a business deal share the profit at the end of a contact. The first received \(\frac{1}{3}\) of the profit and the second \(\frac{2}{3}\) of the remainder. If the third received the remaining N12000.00 how much profit did they share?
- N60 000.00
-
N54 000.00
- N48 000.00
- N42 000.00
The correct answer is: B
Explanation
use "T" to represent the total profit. The first receives \(\frac{1}{3}\) T
remaining, 1 - \(\frac{1}{3}\)
= \(\frac{2}{3}\)T
The seconds receives the remaining, which is \(\frac{2}{3}\) also
\(\frac{2}{3}\) x \(\frac{2}{3}\) = \(\frac{4}{9}\)
The third receives the left over, which is \(\frac{2}{3}\)T - \(\frac{4}{9}\)T = (\(\frac{6 - 4}{9}\))T
= \(\frac{2}{9}\)T
The third receives \(\frac{2}{9}\)T which is equivalent to N12000
If \(\frac{2}{9}\)T = N12, 000
T = \(\frac{12 000}{\frac{2}{9}}\)
Total share[T] = N54, 000
The first receives \(\frac{1}{3}\) of T → \(\frac{1}{3}\) * N54, 000 = N18,000
The second receives \(\frac{4}{9}\) of T → \(\frac{4}{9}\) * N54, 000 = N24,000
The third receives \(\frac{2}{9}\)T which is equivalent to N12000.
Adding the three shares give total profit of N54,000