#### 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 ` 6,400 as profit. Find the profit earned by Vivek.

#### Solution

Since Ratio of their capital is 4 : 5 : 6

∴ Let Ramesh capital be 4x, Vivek capital be 5x

and Sunil capital be 6x

∴Ramesh invested ` 4x "for" 12 "month"

"Vivek invested" ` 5x for 3 month

Sunil invested ` 6x for 6 month

∴Profit is distributed in the ratio

i.e., 4x × 12 : 5x × 3 : 6x × 6

16x : 5x : 12x

16 : 5 : 12

Also 16 + 5 + 12 = 33

Now given that Ramesh profit is ` 6400

∴ Ramesh share in the profit

`=16/33xx"Total Profit"`

`6400=16/33xx"Total Profit"`

Total profit = ` 13,200

Now Vivek share in the profit =`5/33xx13200`

=`Rs 2000`

and Sunil share in the profit = `12/33xx13200`

=`Rs 4800`