Three partners shared the profit in a business in the ratio 6 : 8 : 9. They had partnered for 12 months, 10 months, and 9 months respectively. What was the ratio of their investments?

Question: Three partners shared the profit in a business in the ratio 6 : 8 : 9. They had partnered for 12 months, 10 months, and 9 months respectively. What was the ratio of their investments?

Solution:
Given,
Profit ratio of the three partners
= 6 : 8 : 9
Time of investment
= 12 months : 10 months : 9 months

We know,
Investment × Time = Profit
⇒ Investment = Profit/Time
So, the ratio of their investments will be = (6/12) : (8/10) : (9/9)
= (1/2) : (4/5) : 1

The denominators are 2 and 5.
LCM of 2 and 5 = 10.
Multiplying each term by 10:
Investment ratio = 5 : 8 : 10