Of the three numbers, the ration of the first and the second is 8 : 9 and that of the second and third is 3 : 4. If the product of the first and third number is 2400. then the second number is = ?

$$\eqalign{ & {\text{A}}:{\text{B}}:{\text{C}} \cr & {\text{ }}8:9 \cr & \,\,\,\,\,\,\,\,\,3:4 \cr & \boxed{8:9:12} \cr & 8x:9x:12x \cr & \therefore 8x \times 12x = 2400 \cr & \Rightarrow {x^2} = \frac{{2400}}{{12 \times 8}} \cr & \Rightarrow x = 5 \cr & \therefore {\text{B}} = 9 \times 5 = 45 \cr} $$