Amit, Bittu, and Chinky initiated a business venture

Solution

ATQ, Let, the time for which 'Amit', 'Bittu', and 'Chinky' invested in the business be 'a' months, 'b' months, and 'c' months, respectively. Let, the investment of 'Amit', 'Bittu', and 'Chinky' in the business be, Rs. '8p', Rs. '10p', and Rs. '9p', respectively. Profit share of 'Amit' to 'Bittu' to that of 'Chinky' = (8p × a) :(10p × b) :(9p × c) = 6:5:9 We can say that, (8p × a) :(10p × b) = 6:5 Or, (4/5) × (a/b) = (6/5) Or, (a/b) = (6/5) × (5/4) So, a:b = 3:2 (10p × b) :(9p × c) = 5:9 Or, (10/9) × (b/c) = (5/9) Or, (b/c) = (5/9) × (9/10) So, b:c = 1:2 Let, b = 2q a = (3/2) × b Or, a = (3/2) × 2q So, a = '3q' c = 2b Or, c = 2 × 2q So, c = '4q Ratio of time period of 'Amit' to 'Bittu' to that of 'Chinky' = 3q:2q:4q = 3:2:4