What will come in the place of the question mark (?) in the following equation, if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged? 342 × 18 + 79 − 45 ÷ 3 = ?

Correct — B. Rule: swap + with −, swap × with ÷, then solve the new line by BODMAS.

Printed: 342 × 18 + 79 − 45 ÷ 3
After the swap: 342 ÷ 18 − 79 + 45 × 3

Division first: 342 ÷ 18 = 19
Multiplication next: 45 × 3 = 135

Then left to right: 19 − 79 = −60
and −60 + 135 = 75 → option (b).

Why the others are wrong

• (a)
  65 — 65 is what the swapped line gives if 342 ÷ 18 is taken as 9. The quotient is 19, and 19 − 79 + 135 is 75.
• (c)
  55 — 55 is what the line gives if 45 × 3 is taken as 115. The product is 135, and the expression closes twenty higher.
• (d)
  85 — 85 follows only if the division is read as 29. 342 ÷ 18 is 19, so the line closes ten lower than that.

An interchange item changes the symbols, not the rules. Rewrite the whole line with the swap applied, then solve the new line by ordinary BODMAS — division and multiplication before addition and subtraction, and then left to right.

After the swap the line reads 342 ÷ 18 − 79 + 45 × 3, and every operator printed in the stem has changed.

The commonest loss is doing the swap in your head one symbol at a time while evaluating. Writing the swapped line out costs a few seconds and removes the whole error class.

Key facts

• 342 ÷ 18 = 19.
• 45 × 3 = 135.
• BODMAS still applies after an interchange, because the swap changes which symbol stands where and not the order of operations.

Common traps

• Applying the swap to some symbols and not others, usually the last one in the line.
• Working strictly left to right after the swap and ignoring BODMAS.
• Swapping the numbers when the stem says signs.

No directly related past PYQ was found.