What will come in place of the question mark (?) in the following equation if ‘+’ and ‘×’ are interchanged and ‘–’ and ‘÷’ are interchanged? 16 − 2 × 42 + 13 ÷ 12 = ?

Correct — B.

Rule: rewrite the line with the symbols swapped, then evaluate under BODMAS. '+' becomes '×' and '×' becomes '+'; '−' becomes '÷' and '÷' becomes '−'.

16 − 2 × 42 + 13 ÷ 12
becomes 16 ÷ 2 + 42 × 13 − 12

Now BODMAS on the rewritten line:
16 ÷ 2 = 8
42 × 13 = 546
8 + 546 − 12 = 542 → option (b)

Why the others are wrong

• (a)
  560 — 560 would need the tail to be added. The printed '÷' becomes a minus after the swap, so the last step is − 12, and even + 12 gives only 566.
• (c)
  950 — 950 is far above what the rewritten line allows. Its largest term is 42 × 13 = 546, and the remaining steps only add 8 and take away 12.
• (d)
  762 — 762 would need a product of 766 before the final steps. After the swap the product is fixed at 42 × 13 = 546.

Symbol-interchange questions test one habit: rewrite the line before you calculate. Doing the swap in your head while evaluating is where the marks go.

Two swaps are announced here, + with × and − with ÷. Applying both to 16 − 2 × 42 + 13 ÷ 12 gives 16 ÷ 2 + 42 × 13 − 12.

The swap changes the operators only. Every number keeps its place, so 42 still sits between the second and third operators, and BODMAS then decides the order of work.

Key facts

• After the swap the line reads 16 ÷ 2 + 42 × 13 − 12.
• 16 ÷ 2 = 8 and 42 × 13 = 546, so the total is 8 + 546 − 12 = 542.
• An interchange rewrites operators and leaves the numbers in their printed positions.

Common traps

• Applying only one of the two announced swaps
• Evaluating the rewritten line left to right instead of doing × and ÷ first

No directly related past PYQ was found.