Three partners shared the profit in a business in the ratio 4:6:8. They had partnered for 12 months, 8 months and 6 months respectively. What was the ratio of their investments?

Let their investments be Rs. x for 12 months, Rs. y for 8 months and Rs. z for 6 months respectively.
Then, 12x : 8y : 6z = 4 : 6 : 8
Now, 12x/8y = 4/6   <=>   9x=4y   <=>   y=9x/4
And, 12x/6z = 4/8   <=>   4x=z     <=>    z=4x
Therefore, x : y: z  =  x : 9x/4: 4x  =  4 : 9 : 16