Select the number that will come in the place of the question mark(?), if ‘+’ and ‘ – ‘ are interchanged and ‘×’ and ‘÷’ are interchanged 31 ÷ 3 – 186 × 6 + 17 = ?

Correct — A. Rewrite the line with the symbols swapped, then apply BODMAS to the new line.

Rule: + becomes −, − becomes +, × becomes ÷, ÷ becomes ×.

31 ÷ 3 − 186 × 6 + 17 becomes 31 × 3 + 186 ÷ 6 − 17.

31 × 3 = 93
186 ÷ 6 = 31
93 + 31 = 124 → 124 − 17 = 107 → option (a).

Why the others are wrong

• (b)
  96 — 96 is what the swapped line gives if 186 ÷ 6 is taken as 20. The quotient is 31, because 6 × 31 = 186.
• (c)
  118 — 118 is what the swapped line gives if 186 ÷ 6 is taken as 42. Check it the other way: 6 × 42 = 252, not 186.
• (d)
  103 — 103 is what the line gives if 93 + 31 is added as 120. The sum is 124, and 124 − 17 = 107.

A symbol-interchange sum has two separate jobs, and mixing them is where the marks go.

Job one: rewrite. Physically write out the new line with every symbol replaced. Both swaps apply everywhere in the expression, not just at the first occurrence.

Job two: evaluate the new line under BODMAS. Division and multiplication are done before addition and subtraction, whatever order the symbols appear in. Here that means 31 × 3 and 186 ÷ 6 are both settled before anything is added.

Key facts

• After the swap the expression reads 31 × 3 + 186 ÷ 6 − 17.
• BODMAS settles both × and ÷ before the + and the −, giving 93 and 31.
• 93 + 31 − 17 = 107.

Common traps

• Swapping one pair only. Doing × and ÷ but leaving + and − alone gives 31 × 3 − 186 ÷ 6 + 17 = 79.
• Evaluating left to right after the swap. That gives 29.5, and no option is close to it.
• Swapping in your head and then reading the printed line again, which reinstates the old symbols halfway through.

No directly related past PYQ was found.