# Sonu , one of the 3 partners in a firm , retired from business . His share in profits and losses was 2/5. His share in goodwill of the firm calculated on the basis of 2 years' purchase of superprofit was Rs. 20,000 and the firm's average annual profit was Rs. 40,000 . In the same business normal rate of earning profit is 10%. Calculate the amount of capital invested in the firm.

Sonu's Share of Goodwill is given as Rs 20,000 (calculated on the basis of 2 years' purchase of super profit)

Goodwill of the firm will be Rs 50,000 $(20,000\times \frac{5}{2})$

Now, we know that

$\mathrm{Goodwill}=\mathrm{Super}\mathrm{Profit}\times \mathrm{Number}\mathrm{of}\mathrm{Years}\text{'}\mathrm{Purchase}\phantom{\rule{0ex}{0ex}}\mathrm{i}.\mathrm{e}.50,000=\mathrm{Super}\mathrm{Profit}\times 2\phantom{\rule{0ex}{0ex}}\mathrm{Super}\mathrm{Profit}=\mathrm{Rs}25,000$

Also, we know

$\mathrm{Super}\mathrm{Profit}=\mathrm{Average}\mathrm{Profit}-\mathrm{Normal}\mathrm{Profit}\phantom{\rule{0ex}{0ex}}25,000=40,000-\mathrm{Normal}\mathrm{Profit}\phantom{\rule{0ex}{0ex}}\mathrm{Normal}\mathrm{Profit}=\mathrm{Rs}15,000$

Based on this, the amount of capital invested in the firm can be calculated as,

$\mathrm{Amount}\mathrm{of}\mathrm{Capital}\mathrm{Invested}=\mathrm{Normal}\mathrm{Profit}\times \frac{100}{10}\phantom{\rule{0ex}{0ex}}=15,000\times \frac{100}{10}=\mathrm{Rs}1,50,000$

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