Question

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.

Answer 1

Ramesh:Vivek:Sunil$=4:5:6$

$\therefore$Ramesh$=4x,Vivek$$=5x$$,Sunil$$=6x$

Ramesh invested Rs. $4x$ for $12$ months

Vivek invested Rs. $5x$ for $3$ months

Sunil invested Rs. $6x$ for $6$ months

$\therefore$ Profit distribution ratio=

$4x\times 12:5x\times 3:6x\times 6$

$=16:5:12$

Ramesh got Rs. $6400$, he should get $\frac{16}{16+5+12}$

$\frac{16}{33}$ part of total profit

$\therefore \frac{16}{33}\times$total profit$=6400$

$\therefore$Total profit=Rs. $6403\times \frac{33}{16}$

=Rs. $13200$

$\therefore$Vivek's share=Rs. $\frac{13200\times 5}{33}$=Rs.$2000$

Sunil's share=Rs.$13200\times \frac{12}{33}=$Rs. $4800$