Select the option in which the numbers share the same relationship as that shared by the given pair of numbers. (7, 333) (5, 115) (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.)

Correct — D. Rule: cube the first number, then subtract 10.

7³ = 343, and 343 − 10 = 333
5³ = 125, and 125 − 10 = 115

Apply the same rule to each option's first number:
4³ = 64, and 64 − 10 = 54, which is option (d).

Why the others are wrong

• (a)
  (3, 24) — (3, 24) subtracts 3, not 10: 3³ = 27 and 27 − 3 = 24.
• (b)
  (6, 226) — (6, 226) adds 10 instead of subtracting it: 6³ = 216 and 216 + 10 = 226.
• (c)
  (8, 492) — (8, 492) subtracts 20: 8³ = 512 and 512 − 20 = 492.

The bracketed note is the instruction that matters. Operate on whole numbers, never on their digits, which closes off reading 333 as 3-3-3 and hunting for a digit pattern.

With that shut, run the standard ladder on the numbers you are given: square, cube, a multiple, then a small constant added or taken away.

333 sits just below 343 and 115 just below 125. Both gaps are 10, and that fixes the rule in a single line.

Key facts

• The given pairs follow n³ − 10, since 7³ − 10 = 333 and 5³ − 10 = 115.
• 4³ = 64, so 4³ − 10 = 54.
• The bracketed note forbids splitting a number into digits before operating on it.

Common traps

• Accepting a cube-plus-or-minus rule without checking the constant is the same in both given pairs.
• Breaking 333 into its digits, which the note explicitly forbids.
• Testing the rule against one given pair when the second pair is what pins the constant at 10.

No directly related past PYQ was found.