Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

20 : 49 : 64

Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.
Then, 14x : 8y : 7z = 5 : 7 : 8
Now, 14x/8y=5/7
98x = 40y
y=(49/20)*x
and 14x/7z=5/8
112x = 35z i.e. z = (16/5)x
x:y:z= x: (49/20)x: (16/5)x= 20:49:64