If 3 @ 2= 7 6 @ 3=21 8 @ 2=22 Then 5@4=?

Correct — A.
Rule: a @ b = a × b + (a − b).

Check: 3 @ 2 = 6 + 1 = 7
6 @ 3 = 18 + 3 = 21
8 @ 2 = 16 + 6 = 22

Apply: 5 @ 4 = 20 + 1 = 21 → option (a).

Why the others are wrong

• (b)
  15 — 15 is less than 5 × 4 = 20. With a bigger than b, the rule adds a positive a − b to the product, so the answer must exceed 20.
• (c)
  30 — 30 would need 10 added to the product 20. The rule adds a − b, and 5 − 4 is just 1.
• (d)
  20 — 20 is the product 5 × 4 alone. It drops the + (a − b) term, which the first line shows is needed: 3 × 2 = 6, not 7.

Symbol-operation puzzles hide a rule in a few worked lines. Try the product first, then look at what is left over: 7 − 6 = 1, 21 − 18 = 3, 22 − 16 = 6.

Those leftovers are 3 − 2, 6 − 3 and 8 − 2, so the rule is product plus difference. It can also be written a(b + 1) − b: 3 × 3 − 2 = 7.

Key facts

• a @ b = ab + (a − b) fits all three given lines: 7, 21 and 22.
• When a > b, ab + (a − b) is larger than the product ab.
• Test a candidate rule on every given line before applying it.

Common traps

• Stopping at the product and choosing 20
• Fitting a rule to the first line alone, such as a² − b, which breaks on 6 @ 3

No directly related past PYQ was found.