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

14 : 112 :: 24 : 312 :: 18 : ?

180

Pattern followed is :

 1st term  : 1st term × ( 1st term ÷ 2 + 1)

14 : 112

14  : 14 × ( 14 ÷ 2 + 1)

14 : 14 ×8

14 : 112

& 24 : 312

24  : 24 × ( 24 ÷ 2 + 1)

24 : 24 ×13

24 : 312

Similarly ,

18 : ?

18  : 18 × ( 18 ÷ 2 + 1)

18 : 18 × 10

18 : 180

Hence , 180 is correct answer .