In each of the following questions, a pair of letters is related to a numerical fraction based on their positions in the English alphabet. Determine the logic behind the relationship and apply the same rule to the second pair to find the missing value. JG : 100⁄49 :: TB : ?

Correct — C.
Rule: (position of 1st letter)² ⁄ (position of 2nd letter)².

J = 10 and G = 7, so 10² ⁄ 7² = 100⁄49, as given.
T = 20 and B = 2, so 20² ⁄ 2² = 400⁄4 → option (c).

Why the others are wrong

• (a)
  400⁄5 — 5 in the denominator is not a square. B is the 2nd letter and 2² = 4, so the numerator 400 is right but the denominator must be 4.
• (b)
  650⁄4 — 650 is not a perfect square: 25² = 625 and 26² = 676. T is the 20th letter, so the numerator must be 20² = 400.
• (d)
  709⁄45 — 709⁄45 uses no squares at all. 709 lies between 26² = 676 and 27² = 729, and 45 between 6² = 36 and 7² = 49.

Letter-to-number items turn each letter into its alphabet position (A = 1 … Z = 26), then apply one operation to both numbers.

Find the operation from the example: 100 and 49 are 10² and 7², and J and G are the 10th and 7th letters. The same operation on T (20th) and B (2nd) gives 400 over 4.

Key facts

• Alphabet anchors: E 5, J 10, O 15, T 20, Y 25.
• Squares worth knowing on sight: 7² = 49, 10² = 100, 20² = 400, 25² = 625, 26² = 676.
• B is the 2nd letter, and 2² = 4 is the denominator.

Common traps

• Simplifying 400⁄4 to 100 and then finding no option that shows 100
• Miscounting T as the 19th or 21st letter instead of anchoring it at 20

No directly related past PYQ was found.