13 is related to 119 following a certain logic. Following the same logic, 9 is related to 31. To which of the following is 8 related, following the same logic? (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 — A.

Rule: square the number, then subtract 50.

13² = 169
169 − 50 = 119 ✓
9² = 81
81 − 50 = 31 ✓

The same constant fits both given pairs, so apply it to 8:
8² = 64
64 − 50 = 14 → option (a)

Why the others are wrong

• (b)
  27 — 27 would need 8² − 37. The constant is not free to choose: 13² − 119 and 9² − 31 both come to 50.
• (c)
  24 — 24 is what n² − 5n gives (64 − 40), but that rule sends 13 to 169 − 65 = 104, not 119. Test a candidate rule on both given pairs before using it.
• (d)
  10 — 10 keeps the answer close to the number itself, while the given pairs leap — 13 to 119 and 9 to 31. A jump that large is quadratic, not additive.

The bracketed note is the instruction that matters: operate on the whole number, never on its digits. That bars reading 13 as a 1 and a 3.

With digit games ruled out, work through the small family of whole-number relations in order — multiples, squares, cubes, and each of those with a constant added or subtracted.

Squares are the first thing to try whenever the output is roughly the square of the input. 119 is near 13² = 169 and 31 is near 9² = 81, and both fall short by exactly 50. A constant that repeats across two pairs is the rule.

Key facts

• 13² − 50 = 119, the first relation the question gives.
• 9² − 50 = 31, the second relation, which fixes the constant at 50.
• 8² − 50 = 14, the value asked for.

Common traps

• Fixing the rule from one pair and applying it without checking the second
• Splitting the digits in spite of the bracketed instruction that forbids it

No directly related past PYQ was found.