Of the three numbers, the ratio of the first and the second

Of the three numbers, the ratio 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 :

Let the numbers be a, b and c.
Now, a : b = 8 : 9
b : c = 3 : 4
∴ a : b : c
= 8 × 3 : 9 × 3 : 9 × 4
= 24 : 27 : 36 = 8 : 9 : 12

∴	a	=	b	=	c	= k
	8		9		12

⇒ a = 8k, b = 9k, c = 12k
According to the question,
8k × 12k = 2400

⇒ k² =	2400	= 25
	8 × 12

⇒ k = 5
∴ Second number
= 9k = 9 × 5 = 45