"Akash," "Bishnu," and "Chintu" respectively invested 5:4:6 to launch their businesses. At the end of the year, "Akash" has a profit share of 5:2:4 compared to "Bishnu" and "Chintu." Determine the ratio of "Akash" to "Bishnu" to "Chintu" in terms of investment time.

ATQ, Let, the sum invested by 'Akash', 'Bishnu', and 'Chintu' be Rs. '5x', Rs. '4x', and Rs. '6x', respectively. Let, the time for which 'Akash', 'Bishnu', and 'Chintu' invested in the business be 'p' months, 'q' months, and 'r' months, respectively. ATQ, Ratio of profit share of 'Akash', to 'Bishnu', to that of 'Chintu' = (5x X p) :(4x X q) :(6x X r) = 5:2:4 Or, 5p:4q:6r = 5:2:4 We can say that, 5p:4q = 5:2 Or, (p/q) = (5/2) X (4/5) So, p:q = 2:1 ........(i) 4q:6r = 2:4 Or, (q/r) = (2/4) X (6/4) So, q:r = 3:4 .......(ii) Let, the time for which 'Bishnu' invested the money be '3z' months. So, the time for which 'Akash' invested the money = 2 X 3z = '6z' months {from equation (i) } Time for which 'Chintu' invested the money = (4/3) X 3z = '4z' months {from equation (ii) } So, the ratio of time for which 'Akash', 'Bishnu', and 'Chintu' invested the money = 6z:3z:4z = 6:3:4