What will come in the place of ‘?’ in the following equation, if ‘+’ and ‘–‘ are interchanged and ‘×’ and ‘÷’ are interchanged? 5 – 4 ÷ 9 + 80 × 10 = ?

Correct — B. Rewrite the line with the swapped operators, then apply BODMAS.

Rule: + and − trade places, × and ÷ trade places.

5 – 4 ÷ 9 + 80 × 10
becomes 5 + 4 × 9 – 80 ÷ 10
= 5 + 36 – 8
= 41 – 8 = 33 → option (b)

Why the others are wrong

• (a)
  31 — 31 needs the last term to be 10. After the swap the last term is 80 ÷ 10, which is 8, so the line ends 41 − 8.
• (c)
  35 — 35 needs the last term to be 6. The division 80 ÷ 10 is fixed at 8, whatever order you read the line in.
• (d)
  30 — 30 needs a running total of 38 before the subtraction. The swap gives 5 + 36 = 41, and 41 − 8 = 33.

Sign-interchange questions are two tasks bolted together, and they fail separately.

First the rewrite: change every operator that the instruction names, leaving the numbers untouched. Write the new line out in full.

Then the evaluation: × and ÷ before + and −. Here that means 4 × 9 and 80 ÷ 10 are both settled before either the addition or the subtraction is touched.

Key facts

• After the swap the line reads 5 + 4 × 9 – 80 ÷ 10.
• 4 × 9 = 36 and 80 ÷ 10 = 8.
• 5 + 36 − 8 = 33.

Common traps

• Evaluating strictly left to right, which produces 81 at the second step
• Swapping only + with −, leaving × and ÷ as they are
• Reading 80 × 10 as unchanged because the swap was applied only to the first half

No directly related past PYQ was found.