If a, b, c are three numbers such that a : b = 3 : 4 and b : c = 8 : 9, then what is the ratio a : c?

Given:
$a : b = 3 : 4$

$b : c = 8 : 9$

Step 1: Make b common

LCM of 4 and 8 = 8

So,
$a : b = 3:4 \times 2 = 6:8$
$b : c = 8:9$

Step 2: Combine ratios

$a : b : c = 6 : 8 : 9$

Step 3: Find a : c

$a : c = 6 : 9 = 2 : 3$

Final Answer: 2 : 3