Of three positive numbers, the ratio of 1st and 2nd is 8

Of three positive numbers, the ratio of 1st and 2nd is 8 : 9, that of 2nd and 3rd is 3:4. The product of 1st and 3rd is 2400. The sum of the three numbers is

A : B = 8 : 9
B : C = 3 : 4 = 9 : 12
∴ A : B : C = 8 : 9 : 12
∴ Numbers = 8x, 9x and 12x
∴ 8x × 12x = 2400

⇒ x² =	2400	= 25
	8 × 12

∴ x = √25 = 5
∴ A + B + C = 8x + 9x + 12x
= 29x
= 29 × 5 = 145