What will come in the place of ‘?’ in the following equation, if ‘÷’ and ‘–‘ are interchanged and ‘×’ and ‘+’ are interchanged? 15 × 9 + 7÷ 26 – 13 = ?

Correct — A. Rewrite the line with the symbols exchanged first, then evaluate by BODMAS.

Given: 15 × 9 + 7 ÷ 26 − 13

Apply the swaps — ÷ becomes −, − becomes ÷, × becomes +, + becomes ×:
15 + 9 × 7 − 26 ÷ 13

Divide: 26 ÷ 13 = 2
Multiply: 9 × 7 = 63
Then left to right: 15 + 63 = 78, and 78 − 2 = 76

That is option (a).

Why the others are wrong

• (b)
  84 — Option (b) overshoots. Adding the last term instead of subtracting it gives 15 + 63 + 2 = 80, and dropping it gives 78 — neither route reaches 84.
• (c)
  68 — Option (c) undershoots. The last term after the swap is 26 ÷ 13 = 2 — subtracting an unswapped 13 gives 65 and subtracting 26 gives 52, so no reading lands on 68.
• (d)
  72 — Option (d) is 4 short. Once the swap is applied to all four symbols the line reads 15 + 9 × 7 − 26 ÷ 13 with no free choices left, and it comes to 76.

Symbol-interchange questions test two things, and candidates usually lose the second. First, rewrite the expression with the symbols exchanged. Second, evaluate the new line by BODMAS, not left to right.

The swap is a substitution on paper. It does not change the rules of arithmetic — after ÷ becomes − and × becomes +, the resulting line obeys ordinary precedence.

Writing the swapped line out in full before touching a number is what stops the two pairs getting tangled.

Key facts

• After the interchange, 15 × 9 + 7 ÷ 26 − 13 reads 15 + 9 × 7 − 26 ÷ 13.
• BODMAS applies to the swapped line, so 9 × 7 and 26 ÷ 13 are computed before the addition and subtraction.
• The value is 15 + 63 − 2 = 76.

Common traps

• Evaluating the swapped line left to right instead of by BODMAS
• Swapping one pair of symbols and forgetting the other
• Applying a swap in one direction only, so that − never becomes ÷

No directly related past PYQ was found.