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?

Question: 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?Solution:Let their investments be Tk. x for 14 months, Tk. y for 8 months and Tk. z for 7 months respectively.Then, 14x : 8y : 7z = 5 : 7 : 8.Now, 14x/8y = 5/7⇒ 98x = 40y ∴ y = (49/20) xAnd, 14x/7z = 5/8⇒ 112x = 35z ∴ z = (112/35) x = (16/5) x.x : y : z = x : (49/20) x : (16/5) x = 20 : 49 : 64.