What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged? 14014 × 14 – 10 ÷ 8 + 14 = ?

Correct — C. Rule: swap the symbols first, then apply BODMAS to the new line.

Printed: 14014 × 14 – 10 ÷ 8 + 14
After the swap: 14014 ÷ 14 + 10 × 8 − 14

Divide: 14014 ÷ 14 = 1001
Multiply: 10 × 8 = 80

Then left to right: 1001 + 80 = 1081
1081 − 14 = 1067 → option (c).

Why the others are wrong

• (a)
  1062 — A slip in the last step. After the swap the line is 1001 + 80 − 14, and 1081 − 14 is 1067; reaching 1062 would mean taking 19 off.
• (b)
  1063 — 1063 is 1081 − 18. Only one subtraction survives the swap, of 14, because the printed − sits in front of 10 and becomes a +.
• (d)
  1064 — 1064 is 1081 − 17. Writing the swapped line out in full guards against it: 14014 ÷ 14 + 10 × 8 − 14 leaves exactly one subtraction.

Two things happen in this item and they must not be merged. First the swap rewrites the expression: every + becomes −, every − becomes +, every × becomes ÷ and every ÷ becomes ×.

Only then does BODMAS apply, and it applies to the rewritten line. Division and multiplication are settled first, left to right, then addition and subtraction, also left to right.

Writing the swapped expression on its own line before touching any arithmetic is what stops the two stages contaminating each other.

Key facts

• The swap rewrites the expression and does not change the order of operations.
• 14014 ÷ 14 = 1001, which is the step that makes the rest of the line easy.
• After the swap the line reads 14014 ÷ 14 + 10 × 8 − 14.
• That evaluates as 1001 + 80 − 14 = 1067.

Common traps

• Applying BODMAS to the printed line and swapping the symbols afterwards.
• Swapping only one of the two pairs, usually leaving × and ÷ untouched.
• Treating the − in front of 10 as a subtraction after it has become a +.

No directly related past PYQ was found.