Question

Given the profit share distribution as follows:
Keeping the family's profit unchanged and after giving everyone an equal share of the profit, find what fraction of the total profit can be reinvested.

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{5}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B $\frac{1}{3}$

As per the given question, you need to reinvest in such a way that your remaining profit is equal to that of your family's existing profit.

Hence, after reinvesting,
Family's profit = Your profit = $\frac{16}{7}$x + $\frac{394}{7}$

Reinvested amount
= Total profit - 2 × ($\frac{16}{7}$x + $\frac{394}{7}$)

= $\frac{48}{7}$x + $\frac{1182}{7}$ - $\frac{32}{7}$x - $\frac{788}{7}$

= ($\frac{48}{7}$x - $\frac{32}{7}$x) + $\frac{1182}{7}$ - $\frac{788}{7}$

= $\frac{16}{7}$x + $\frac{394}{7}$

Total profit = $\frac{48}{7}$x + $\frac{1182}{7}$
= (3 × $\frac{16}{7}$x) + (3 × $\frac{394}{7}$)
= 3 × ($\frac{16}{7}$x + $\frac{394}{7}$)
= 3 × Reinvested amount

$\therefore$ Reinvested amount is $\frac{1}{3}$ times of total profit.