Question

If you need to reinvest a part of your profit keeping the family's profit unchanged, the fraction of total profit that can be reinvested is .

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{1}{5}$

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 = $\frac{7}{5}$x + $\frac{91}{5}$
Reinvested amount = Total profit - 2 $\times$ ($\frac{7}{5}$x + $\frac{91}{5})$
= $\frac{21}{5}$x + $\frac{273}{5}$ - ( $\frac{14}{5}$x + $\frac{182}{5})$
= ($\frac{21}{5}$x - $\frac{14}{5}$x) + ($\frac{273}{5}$ - $\frac{182}{5})$
= $\frac{7}{5}$x + $\frac{91}{5}$

Total profit = $\frac{21}{5}$x + $\frac{273}{5}$
= (3 $\times$ $\frac{7}{5}$x) + (3 $\times$ $\frac{91}{5})$
= 3 $\times$ ($\frac{7}{5}$x + $\frac{91}{5})$
= 3 × Reinvested amount

$\therefore$ Reinvested amount = $\frac{1}{3}$ × Total profit