What will come in the place of ‘?’ in the following equation, if ‘+’ and ‘–‘ are interchanged and ‘×’ and ‘÷’ are interchanged? 4 ÷ 6 + 91 × 7 − 5 = ?

Correct — C. Rewrite the line with both swaps, then apply BODMAS to the new line.

Rule: + ↔ − and × ↔ ÷ ; precedence is unchanged.

4 ÷ 6 + 91 × 7 − 5
becomes 4 × 6 − 91 ÷ 7 + 5

4 × 6 = 24
91 ÷ 7 = 13

24 − 13 + 5, taken left to right: 24 − 13 = 11, then 11 + 5 = 16 → option (c).

Why the others are wrong

• (a)
  12 — 12 is not reachable here. The fully swapped line gives 16; swapping only × and ÷ gives 4 × 6 + 91 ÷ 7 − 5 = 32; swapping only + and − leaves a large negative. None of them is 12.
• (b)
  21 — 21 needs 91 ÷ 7 to be 8, since 24 − 8 + 5 = 21. The division is exact — 7 × 13 = 91 — so the middle term is 13.
• (d)
  17 — 17 needs 91 ÷ 7 to be 12, since 24 − 12 + 5 = 17. Again the division is exact at 13.

Sign-interchange items ask you to rewrite before you compute. Change every symbol the stem names, in both directions of each pair, and only then evaluate.

The new line obeys ordinary BODMAS: division and multiplication first, then addition and subtraction left to right. The swap alters which symbols appear, never the precedence.

Writing the rewritten expression on the rough sheet keeps the original and swapped versions from blending — the single most common way this easy mark is lost.

Key facts

• After the interchange the expression reads 4 × 6 − 91 ÷ 7 + 5.
• 4 × 6 = 24 and 91 ÷ 7 = 13.
• 24 − 13 + 5 = 16, working left to right.

Common traps

• Swapping one pair of symbols and forgetting the other — both + / − and × / ÷ change here.
• Evaluating 24 − 13 + 5 as 24 − 18 — addition and subtraction run left to right.
• Dividing 91 by 7 carelessly — the answer is 13, and both 8 and 12 lead straight to a listed option.

No directly related past PYQ was found.