JAMB - Mathematics (2021 - No. 15)
Three brothers in a business deal share the profit at the end of a contract. 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
Paliwanag
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 \(\frac{2}{3}\) x \(\frac{4}{9}\)
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 = \(\frac{12 000}{\frac{2}{9}}\)
= N54, 000
remaining, 1 - \(\frac{1}{3}\)
= \(\frac{2}{3}\)T
The seconds receives the remaining, which is \(\frac{2}{3}\) also
\(\frac{2}{3}\) x \(\frac{2}{3}\) x \(\frac{4}{9}\)
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 = \(\frac{12 000}{\frac{2}{9}}\)
= N54, 000