Select the option that is related to the fourth number in the same way as the first number is related to the second number and the fifth number is related to the sixth number.

8 : 24 : : ? : 52 : : 18 : 114

12

8 : 24 : : ? : 52 : : 18 : 114

The logic followed here is :

[Ist number × (Ist number + 1 ) ] ÷ 3 = IInd number

As

[8 × (8 + 1 ) ] ÷ 3

= (8 × 9) ÷ 3

= 72 ÷ 3

= 24

And

18 : 114

[18 × (18 + 1 ) ] ÷ 3

= (18 × 19) ÷ 3

= 342 ÷ 3

= 114

Similarly

? : 52

[A × (A + 1 ) ] ÷ 3= 52

[A × (A + 1 ) ]  = 52 ×  3

[A × (A + 1 ) ] = 156

A²  + A =  156

Therefore A will be the value of 12

12² + 12

144 + 12 = 156(hence proved)