What will come in the place of ‘?’ in the following equation, if ‘+’ and ‘–‘ are interchanged and ‘×’ and ‘÷’ are interchanged? 49 × 7 – 6 ÷ 8 +13 =

Correct — A. Rule: swap every symbol first, then apply BODMAS to what you have written.

× becomes ÷, ÷ becomes ×, + becomes − and − becomes +.

So 49 × 7 − 6 ÷ 8 + 13 rewrites as 49 ÷ 7 + 6 × 8 − 13.

49 ÷ 7 = 7
6 × 8 = 48
7 + 48 = 55
55 − 13 = 42

The value is 42, which is option (a).

Why the others are wrong

• (b)
  37 — Working the swapped chain left to right instead of by BODMAS gives 7 + 6 = 13, then 13 × 8 = 104, then 104 − 13 = 91. Neither route reaches 37.
• (c)
  43 — The chain closes 7 + 48 = 55 and 55 − 13 = 42. Reaching 43 would need the last step to be 55 − 12, so it is an arithmetic slip rather than a different reading of the rule.
• (d)
  32 — A half-done swap, changing × and ÷ but leaving + and −, gives 49 ÷ 7 − 6 × 8 + 13 = −28, not 32. The instruction swaps both pairs, and the full swap gives 42.

A sign-interchange item tests two habits at once. First, that you rewrite every occurrence of the swapped symbols rather than the first one you notice. Second, that you then apply BODMAS to the rewritten expression and not to the printed one.

The order is not negotiable. Swap, then evaluate. Evaluating first and adjusting afterwards fails because the operations bind at different strengths, so changing a symbol changes what binds to what.

After the swap the expression is ordinary: division and multiplication settle before addition and subtraction.

Key facts

• Interchanging means every occurrence changes, in both directions of each pair.
• The swapped expression here is 49 ÷ 7 + 6 × 8 − 13.
• BODMAS applies after the swap, settling 49 ÷ 7 = 7 and 6 × 8 = 48 first.
• The swapped expression evaluates to 42.

Common traps

• Swapping one pair of symbols and leaving the other pair as printed
• Evaluating the swapped chain left to right, which gives 91 here
• Applying BODMAS to the printed expression and then trying to correct the result

No directly related past PYQ was found.