Study the given pattern carefully and select the number that can replace the question mark (?) in it.
(5, 14, 3)
(3, 24, 7)
(9, 30, ?)
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13- Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)

For each ordered triple $$(a,b,c)$$ observe the relation between the first, second and third numbers.

Compute the difference between the second and first numbers for the given triples:

$$b-a \;=\;14-5=9 \quad\text{when }(a,b,c)=(5,14,3)$$
$$b-a \;=\;24-3=21\quad\text{when }(a,b,c)=(3,24,7)$$

Now compare these differences with the third numbers:

$$9 = 3 \times 3 \qquad\text{and}\qquad 21 = 7 \times 3$$

The common pattern is therefore

$$b-a = 3c \quad\Longrightarrow\quad c = \frac{b-a}{3}$$

Apply this rule to the third triple $$(9,30,?)$$:

$$c = \frac{b-a}{3} = \frac{30-9}{3} = \frac{21}{3} = 7$$

Hence the missing number is $$7$$.

Option A which is: 7