Ramesh, Vivek and Sunil started a business by investing capitals in the ratio $4 : 5 : 6$ . After $3$ months Vivek withdrew all his capital and after $6$ months Sunil withdrew all his capital from the business. At the end of the year Ramesh received Rs $6, 400$ as profit. Find the profit earned by Vivek.

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Solution

Ramesh:Vivek:Sunil $= 4 : 5 : 6$
$∴$ Ramesh $= 4 x, V i v e k$ $= 5 x$ $, S u n i l$ $= 6 x$
Ramesh invested Rs. $4 x$ for $12$ months
Vivek invested Rs. $5 x$ for $3$ months
Sunil invested Rs. $6 x$ for $6$ months
$∴$ Profit distribution ratio=
$4 x \times 12 : 5 x \times 3 : 6 x \times 6$
$= 16 : 5 : 12$
Ramesh got Rs. $6400$ , he should get $\frac{16}{16 + 5 + 12}$
$\frac{16}{33}$ part of total profit
$∴ \frac{16}{33} \times$ total profit $= 6400$
$∴$ Total profit=Rs. $6403 \times \frac{33}{16}$
=Rs. $13200$
$∴$ Vivek's share=Rs. $\frac{13200 \times 5}{33}$ =Rs. $2000$
Sunil's share=Rs. $13200 \times \frac{12}{33} =$ Rs. $4800$

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