What will come in the place of ‘?’ in the following equation, if ‘÷’ and ‘–‘ are interchanged and ‘×’ and ‘+’ are interchanged? 8 + 6 ÷ 51 – 17 × 13 = ?

Correct — A. Rule: rewrite with the swapped symbols, then apply BODMAS. Here ÷ swaps with – and × swaps with +.

Given: 8 + 6 ÷ 51 – 17 × 13
After the swap:
8 × 6 – 51 ÷ 17 + 13

Multiplication and division first:
8 × 6 = 48
51 ÷ 17 = 3

Then left to right:
48 – 3 = 45
45 + 13 = 58 → option (a)

Why the others are wrong

• (b)
  32 — 32 is 48 – 3 – 13, the last term subtracted. After the swap the × standing before 13 becomes a +, so 13 must be added.
• (c)
  63 — 63 would need 48 – 3 to come to 50. It comes to 45, and 45 + 13 = 58.
• (d)
  71 — 71 would need the first product to be 61, but the swapped line fixes it at 8 × 6 = 48.

The pairing here is not the usual one. It is ÷ with – and × with +, so read the instruction twice before touching the numbers.

The rewrite is mechanical: every ÷ becomes –, every – becomes ÷, every × becomes +, every + becomes ×. Do it once, on paper, for the whole line.

What is left is an ordinary BODMAS sum — brackets, then × and ÷ left to right, then + and – left to right.

Key facts

• The swap turns 8 + 6 ÷ 51 – 17 × 13 into 8 × 6 – 51 ÷ 17 + 13.
• 51 ÷ 17 = 3 exactly.
• 48 – 3 + 13 = 58.

Common traps

• Swapping + with – out of habit, when this question pairs + with ×
• Leaving the final term subtracted, which gives 32
• Working straight left to right, so 8 × 6 – 51 is computed before the division

No directly related past PYQ was found.