Select the number that will come in the place of the question mark(?), if ‘+’ and ‘ – ‘ are interchanged and ‘×’ and ‘÷’ are interchanged 61 – 42 × 6 ÷ 9 + 27 = ?

Correct — A. Rule: rewrite the line with the symbols swapped, then apply BODMAS. Plus trades with minus, and multiplication trades with division.

61 − 42 × 6 ÷ 9 + 27
becomes 61 + 42 ÷ 6 × 9 − 27

Division and multiplication first, left to right.
42 ÷ 6 = 7
7 × 9 = 63

Then addition and subtraction, left to right.
61 + 63 = 124
124 − 27 = 97 — option (a)

Why the others are wrong

• (b)
  101 — 101 sits four above the correct total. It would need the middle block to come to 67, and 42 ÷ 6 × 9 is exactly 63.
• (c)
  89 — 89 would need the middle block to be 55. Worked left to right, 42 ÷ 6 = 7 and 7 × 9 = 63, so the line is 61 + 63 − 27.
• (d)
  84 — 84 falls thirteen below the correct total. The three stages are fixed: 42 ÷ 6 = 7, then 7 × 9 = 63, then 61 + 63 − 27 = 97.

Two independent errors are being probed. The first is failing to do the swap at all. The second is forgetting that BODMAS governs the rewritten line, so the division and multiplication in the middle are settled before the outer addition and subtraction.

Rewrite the line on paper. The swap costs five seconds and removes the commonest slip in this section.

Order within the same tier matters too: 42 ÷ 6 × 9 is 63, whereas 42 ÷ (6 × 9) would be well under 1.

Key facts

• After the swap the line reads 61 + 42 ÷ 6 × 9 − 27.
• Worked left to right, 42 ÷ 6 × 9 = 63.
• 61 + 63 − 27 = 97.

Common traps

• Swapping the symbols correctly and then working the new line strictly left to right
• Reading 42 ÷ 6 × 9 as 42 ÷ 54 by multiplying before dividing

No directly related past PYQ was found.