Select the number that will come in the place of the question mark (?), if ‘+’ and ‘ – ‘ are interchanged and ‘×’ and ‘÷’ are interchanged 121 × 11 – 28 ÷ 3 + 17 = ?

Correct — A. Rule: interchange + with − and × with ÷, then evaluate the new line by BODMAS.

121 × 11 – 28 ÷ 3 + 17
becomes 121 ÷ 11 + 28 × 3 − 17

121 ÷ 11 = 11
28 × 3 = 84
11 + 84 − 17 = 78, which is option (a).

Why the others are wrong

• (b)
  91 — 91 would need the middle term to be 97, since 11 + 97 − 17 = 91. The middle term is 28 × 3 = 84.
• (c)
  64 — 64 would need the middle term to be 70, since 11 + 70 − 17 = 64. Again, 28 × 3 = 84.
• (d)
  85 — 85 would need the first term to be 18, since 18 + 84 − 17 = 85. The first term is 121 ÷ 11 = 11.

After the swap the line always collapses to three terms joined by one plus and one minus: a division, a multiplication and a bare number.

Settle the division and the multiplication first and what is left is a sum you can do in your head — here 11, 84 and 17.

That structure also lets you test an option without redoing the arithmetic: any value you cannot build from 11, 84 and 17 with a + and a − is out.

Key facts

• After the swap the expression reads 121 ÷ 11 + 28 × 3 − 17.
• 121 ÷ 11 = 11 and 28 × 3 = 84, so the value is 11 + 84 − 17 = 78.
• The four operators move. Every number keeps its place in the line.

Common traps

• Interchanging the numbers around the signs instead of the signs themselves.
• Adding before multiplying once the line has been rewritten.
• Swapping + with × or − with ÷, which the instruction does not ask for.

No directly related past PYQ was found.