Which two numbers need to be swapped to make this equation correct? 20 ÷ 5 × 3 + 10 − 4 = 20

Correct — D.
Rule: swap the pair, then work ÷ and × left to right before + and −.

As printed: 20 ÷ 5 × 3 + 10 − 4
= 4 × 3 + 10 − 4
= 12 + 10 − 4 = 18, not 20.

Swap 4 and 5: 20 ÷ 4 × 3 + 10 − 5
= 5 × 3 + 10 − 5
= 15 + 10 − 5 = 20, which balances → option (d).

Why the others are wrong

• (a)
  5 and 10 — Swapping 5 and 10 gives 20 ÷ 10 × 3 + 5 − 4 = 6 + 5 − 4 = 7, nowhere near 20.
• (b)
  3 and 4 — Swapping 3 and 4 gives 20 ÷ 5 × 4 + 10 − 3 = 16 + 10 − 3 = 23. Close, but the equation needs exactly 20.
• (c)
  20 and 10 — Swapping 20 and 10 fails whichever 20 moves: 10 ÷ 5 × 3 + 20 − 4 = 22, and sending 10 to the right side leaves 28 = 10.

A swap puzzle is arithmetic in disguise. Work the equation as printed first to learn the gap: it gives 18, two short of 20.

Then look for a swap worth exactly +2. Putting 4 in the divisor turns 20 ÷ 5 × 3 = 12 into 20 ÷ 4 × 3 = 15, a gain of 3. Putting 5 in the subtraction costs 1 extra. Net change: +3 − 1 = +2.

Key facts

• As printed, 20 ÷ 5 × 3 + 10 − 4 = 18.
• Swapping 4 and 5 gives 20 ÷ 4 × 3 + 10 − 5 = 20.
• Division and multiplication are worked left to right before addition and subtraction.

Common traps

• Skipping the as-printed value, so every option has to be worked in full without a target gap
• Accepting a near miss: swapping 3 and 4 gives 23, not 20

No directly related past PYQ was found.