Select the option in which the numbers shares the same relationship as that shared by the numbers in the given set.
(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)

(46, 138, 414)

(46, 138, 414)

Second number = $$3\times\ first\ number$$ = $$3\times46$$ = 138

Third number = $$3\times\ second\ number$$ = $$3\times138$$ = 414

Option (a) (38, 114, 342)

Second number = $$3\times38$$ = 114

Third number =$$3\times114$$ = 342

The above-given logic is available here. So this is the correct answer.

Option (b) (42, 126, 504)

Second number = $$3\times42$$ = 126

Third number = $$3\times126$$ = 378

The above-given logic is not available here. So this is not the correct answer.

Option (c) (52, 156, 624)

Second number = $$3\times52$$ = 156

Third number = $$3\times156$$ = 468

The above-given logic is not available here. So this is not the correct answer.

Option (d) (56, 224, 896)

Second number = $$3\times56$$ = 168

Third number = $$3\times168$$ = 504

The above-given logic is not available here. So this is not the correct answer.