What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 272 × 16 + 97 − 23 ÷ 4 = ?

Correct — B. Rule: swap the symbols, not the numbers, then apply BODMAS to the rewritten line.

272 × 16 + 97 − 23 ÷ 4
becomes 272 ÷ 16 − 97 + 23 × 4

272 ÷ 16 = 17
23 × 4 = 92
17 − 97 + 92 = 12, which is option (b).

Why the others are wrong

• (a)
  22 — 22 is what you get by swapping × and ÷ but leaving + and − as printed: 272 ÷ 16 + 97 − 23 × 4 = 17 + 97 − 92 = 22. Both pairs have to move.
• (c)
  2 — 2 would need 272 ÷ 16 to come out as 7. It is 17, and 17 − 97 + 92 = 12.
• (d)
  21 — 21 would need 23 × 4 to come out as 101. It is 92, and 17 − 97 + 92 = 12.

The instruction changes the four signs and nothing else. Rewrite the whole line with the new signs on paper first, and only then start calculating.

The rest is ordinary BODMAS: division and multiplication are settled before addition and subtraction, wherever they sit in the line.

So 272 ÷ 16 and 23 × 4 are both computed before the − and the + are applied, which is why the answer is a small number rather than a large one.

Key facts

• Interchanging + with − and × with ÷ moves the signs only. Every number stays where it is.
• BODMAS still applies after the swap, so 272 ÷ 16 and 23 × 4 are evaluated first.
• 272 ÷ 16 = 17 and 23 × 4 = 92, so 17 − 97 + 92 = 12.

Common traps

• Swapping one pair and forgetting the other, which lands exactly on 22.
• Working left to right after the swap instead of applying BODMAS.
• Rewriting the numbers instead of the signs.

No directly related past PYQ was found.