What will come in place of the question mark (?) in the following equation if ‘+’ and ‘ב are interchanged and ‘−’ and ‘÷’ are interchanged? 27 − 6 + 4 × 8 ÷ 6 = ?

Correct — A. Substitute the symbols first, then apply BODMAS to the new expression.

Rule: '+' becomes '×', '×' becomes '+', '−' becomes '÷', '÷' becomes '−'.

So 27 − 6 + 4 × 8 ÷ 6 rewrites as 27 ÷ 6 × 4 + 8 − 6.

27 ÷ 6 = 4.5
4.5 × 4 = 18
18 + 8 = 26
26 − 6 = 20 → option (a)

Why the others are wrong

• (b)
  18 — 18 is 27 ÷ 6 × 4 and nothing more — the running value before + 8 and − 6 are applied.
• (c)
  16 — 16 is 18 − 8 + 6. The swap sends '×' to '+' and '÷' to '−', so the last two operators are plus then minus, in that order.
• (d)
  22 — 22 would need 27 ÷ 6 × 4 to come to 20. It comes to 18, because 27 ÷ 6 = 4.5 and not a whole number.

Two substitutions run at once here and they are independent. '+' and '×' swap with each other, and '−' and '÷' swap with each other.

Rewrite the whole line before calculating anything. Converting one operator at a time while evaluating is where the marks go.

Then BODMAS on the rewritten line: division and multiplication first, left to right, then addition and subtraction, left to right. The intermediate 4.5 is not a whole number and does not need to be — the final total still lands on an integer.

Key facts

• After the swap the line reads 27 ÷ 6 × 4 + 8 − 6.
• Division and multiplication are settled left to right before any addition or subtraction.
• 27 ÷ 6 × 4 = 18, and 18 + 8 − 6 = 20.

Common traps

• Swapping one pair of symbols and leaving the other pair as printed.
• Rounding 27 ÷ 6 to 4 or to 5 before multiplying.
• Applying the swap to your answer rather than to the question, so + 8 − 6 comes out as − 8 + 6.

No directly related past PYQ was found.