Three partners shared the profit in a business in the ratio 5 : 6 :7 . They had partnered for 12 months, 10 months, and 8 months respectively. What was the ratio of their investments?

#### Solution

Let the ratio of investments of the three partners be p : q : r.

They partnered for 12 months, 10 months, and 8 months respectively.

∴ The profit shared by the partners will be in proportion of the product of capital invested and their respective time periods.

∴ 12 × p : 10 × q : 8 × r = 5 : 6 : 7

Now, `(12"p")/(10"q") = 5/6`

∴ `"p"/"q" = 50/72` ...................(i)

and `(10"q")/(8"r") = 6/7`

∴ `"q"/"r" = 48/70 = 24/35 xx 3/3`

∴ `"q"/"r" = 72/105` .................(ii)

From (i) & (ii), we have

p : q : r = 50 : 72 : 105

∴ The ratio of their investments was 50 : 72 : 105.