What will come in place of the question mark (?) in the following equation if ‘+’ and ‘−‘ are interchanged and ‘×’ and ‘÷’ are interchanged? 15 − 7 ÷ 4 + 36 × 9 = ?

Correct — B. Swap the symbols first, then work the new line by BODMAS.

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

15 − 7 ÷ 4 + 36 × 9 rewrites as 15 + 7 × 4 − 36 ÷ 9

Multiply and divide first: 7 × 4 = 28, and 36 ÷ 9 = 4
Then left to right: 15 + 28 = 43, and 43 − 4 = 39

So the missing value is 39, option (b).

Why the others are wrong

• (a)
  42 — 42 would need the line to end in − 1. After the swap it ends in − 36 ÷ 9, which is − 4, so the total lands on 39 and not 42.
• (c)
  34 — 34 comes from subtracting 9 instead of 36 ÷ 9: 15 + 28 − 9 = 34. The division outranks the subtraction and must be done first.
• (d)
  40 — 40 is one too high. It appears if 36 ÷ 9 is taken as 3 rather than 4, giving 15 + 28 − 3.

A sign-substitution question asks you to rewrite the line, then solve it. The swap is an instruction about the printed symbols only.

Do the rewrite on paper before any arithmetic. The usual loss is solving the printed line by BODMAS and swapping the operators afterwards, which is a different calculation altogether.

Once rewritten, ordinary precedence applies: brackets, then division and multiplication left to right, then addition and subtraction left to right.

Key facts

• The swap touches operators only — the digits and their order never move.
• BODMAS applies to the line after the swap, not to the line as printed.
• Here − becomes + and ÷ becomes ×, so 7 ÷ 4 turns into 7 × 4 = 28.

Common traps

• Applying BODMAS to the printed line and swapping the operators afterwards
• Swapping only one of the two given pairs
• Reading the rewritten line left to right and ignoring precedence

No directly related past PYQ was found.