In the given number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Select the number-pair in which the numbers are related in the same way as are the numbers of the given number-pairs.

(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.)

(19, 200)

(15, 160)

The correct answer is (22, 230).

Pattern / Logical Rule:

In the given number-pairs, the second number is obtained by adding 1 to the first number and then multiplying the result by 10.

$\text{Second Number}=(\text{First Number}+1)\times 10$

Let's verify this mathematical relationship with the given number-pairs:

1. For the pair (19, 200):

$(19+1)\times 10=20\times 10=200$

2. For the pair (15, 160):

$(15+1)\times 10=16\times 10=160$

Now, let's test each option using the established rule:

Option 1: (23, 300)

$(23+1)\times 10=24\times 10=240\ne 300$
(Incorrect)

Option 2: (22, 230)

$(22+1)\times 10=23\times 10=230$
(Correct)

Option 3: (25, 250)

$(25+1)\times 10=26\times 10=260\ne 250$
(Incorrect)

Option 4: (18, 200)

$(18+1)\times 10=19\times 10=190\ne 200$
(Incorrect)

Therefore, the pair (22, 230) follows the exact same rule as the given number-pairs.