A, B and C started a business by investing in the ratio 4 : 3 : 2. At the end of the year the profit earned was distributed among them in the ratio 8 : 9 : 10. Find the ratio of the durations of their investment.

2 : 3 : 5

Profit = Investment × Time

Time = Profit/Investment

T1/T2 = (P1/P2)/(I1/I2) = P1*I2/P2*I1

Ratio of Investment of A to B = 4:3

Ratio of Profit of A to B = 8:9

Ratio of Time A to B = 8*3/9*4 = 2:3

Ratio of Investment of B to C = 3:2

Ratio of Profit of B to C = 9:10

Ratio of Time B to C = 9*2/10*3 = 3:5

The correct answer is Option (2) → 2 : 3 : 5