Select the set in which the numbers are related in the same way as are the numbers of the following sets.

(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 /deleting /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)

(144, 12, 24)

(216, 18, 36)

The correct option is (324, 27, 54).

Step-by-step Explanation:

Let's analyze the relationship between the three numbers $(A,B,C)$ in the given sets:

First given set: $(144,12,24)$

1. Observe the third number ($C$) and the second number ($B$):

$24÷2=12$

2. Now multiply the result by the second number ($B$):

$12\times 12=144$ (which is the first number, $A$)

Alternatively, the pattern is: $A=B\times (C÷2)$

Second given set: $(216,18,36)$

1. Divide the third number by 2:

$36÷2=18$

2. Multiply by the second number:

$18\times 18=216$ (which is the first number, $A$)

Checking the options using the same rule $A=B\times (C÷2)$:

For the set (324, 27, 54):

1. Divide the third number ($54$) by 2:

$54÷2=27$

2. Multiply by the second number ($27$):

$27\times 27=324$

This matches the first number ($324$) perfectly.

Hence, the set (324, 27, 54) follows the exact same logic as the given sets.