What will come in the place of ‘?’ in the following equation, if ‘÷’ and ‘–‘ are interchanged and ‘×’ and ‘+’ are interchanged? 7 + 4 ÷18 – 3 × 2 = ?

Correct — C. Swap the symbols first, then apply BODMAS to the line that results.

The instruction swaps ÷ with − and × with +. Reading 7 + 4 ÷ 18 − 3 × 2 symbol by symbol, + becomes ×, ÷ becomes −, − becomes ÷, and × becomes +.

The expression is now 7 × 4 − 18 ÷ 3 + 2.

18 ÷ 3 = 6
7 × 4 = 28
28 − 6 + 2 = 24 → option (c).

Why the others are wrong

• (a)
  18 — Under the swapped line 7 × 4 − 18 ÷ 3 + 2, the 18 is divided by 3 before any addition or subtraction, so it cannot survive to be the answer. 18 is simply a number carried over unchanged from the original.
• (b)
  16 — The swapped line reduces to the three terms 28, 6 and 2. Combined with the signs the swap produces, they give 24, and no reordering of them reaches 16.
• (d)
  20 — 20 is 28 − (6 + 2) — the mistake of pulling the trailing + 2 inside the subtraction. Once × and ÷ are cleared, addition and subtraction run strictly left to right.

Symbol-interchange questions test two things at once: substituting the operators correctly, and then applying BODMAS to the rewritten line.

The substitution runs both ways. 'Interchanged' means every ÷ becomes − and every − becomes ÷ in the same pass, and likewise for × and +.

Once rewritten, the line is ordinary arithmetic. Multiplication and division are cleared first, and the remaining addition and subtraction are worked left to right.

Key facts

• Interchanging ÷ with − and × with + turns 7 + 4 ÷ 18 − 3 × 2 into 7 × 4 − 18 ÷ 3 + 2.
• BODMAS clears 18 ÷ 3 = 6 and 7 × 4 = 28 before any subtraction.
• 28 − 6 + 2 = 24, working the addition and subtraction from the left.

Common traps

• Swapping in one direction only, so ÷ becomes − but − is left as it is
• Solving the rewritten line strictly left to right and ignoring BODMAS
• Treating a trailing + 2 as part of the subtraction before it, which gives 20

No directly related past PYQ was found.