What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 2736 × 8 – 55 + 105 ÷ 2 = ?

Correct — D. Rule: '+' and '−' trade places, and '×' and '÷' trade places.

Rewrite the line sign by sign:
2736 × 8 − 55 + 105 ÷ 2
becomes 2736 ÷ 8 + 55 − 105 × 2

Now apply BODMAS to the rewritten line:
2736 ÷ 8 = 342
105 × 2 = 210
342 + 55 − 210 = 187 → option (d)

Why the others are wrong

• (a)
  177 — 177 is 187 with the tens digit altered. The three terms of the rewritten line are fixed at 342, 55 and 210, and 342 + 55 = 397, from which 210 leaves 187.
• (b)
  137 — 137 would need the first term to be 292 instead of 342. That division is exact: 8 × 342 = 2736, with nothing left over.
• (c)
  127 — 127 would need 270 taken off at the end. The final term is 105 × 2 = 210, because the swap turns the printed divide into a multiply.

Two rewrites and one evaluation. Swap every symbol first, on paper, and only then read the new line under BODMAS. The commonest loss here is starting the arithmetic before the rewrite is finished.

Both pairs are two-way. The printed '×' becomes '÷' and the printed '÷' becomes '×', so a line that ended in a division now ends in a multiplication. That is what turns a small final term into a large one here.

The numbers never move. 2736, 8, 55, 105 and 2 stay in place — only the symbols between them change.

Key facts

• After the swap the line reads 2736 ÷ 8 + 55 − 105 × 2.
• 2736 ÷ 8 = 342 and 105 × 2 = 210.
• 342 + 55 − 210 = 187.
• An interchange changes operators only, so every number keeps its place.

Common traps

• Swapping the plus and minus and forgetting that times and divide swap as well
• Leaving the final division as a division, which turns 210 into 52.5
• Working the rewritten line left to right instead of by BODMAS

No directly related past PYQ was found.