Which two numbers (not digits) should be interchanged to make the given equation correct? 48 ÷ 3 + 12 × 4 – 6 × 7 + 21 = 27

Correct — C. Rule: interchange the two numbers, then evaluate by BODMAS — division and multiplication before addition and subtraction.

Swap 3 and 4 and the line reads:
48 ÷ 4 + 12 × 3 – 6 × 7 + 21

48 ÷ 4 = 12
12 × 3 = 36
6 × 7 = 42
12 + 36 – 42 + 21 = 27 → option (c)

Why the others are wrong

• (a)
  12 and 21 — Swapping 12 and 21 gives 48 ÷ 3 + 21 × 4 – 6 × 7 + 12 = 16 + 84 – 42 + 12 = 70. The 21 lands inside a multiplication, which inflates the total instead of cutting it.
• (b)
  4 and 7 — This reads 48 ÷ 3 + 12 × 7 – 6 × 4 + 21 = 16 + 84 – 24 + 21 = 97. Pulling 4 out of the multiplied pair and pushing 7 into it moves the value further from 27, not closer.
• (d)
  3 and 6 — Now 48 ÷ 6 + 12 × 4 – 3 × 7 + 21 = 8 + 48 – 21 + 21 = 56. The division does shrink, but 12 × 4 is left untouched, and that 48 is the term the correct swap cuts to 36.

The instruction says numbers, not digits — you move whole terms such as 3 and 4, never the individual digits inside 48 or 21.

Fix the size of the gap first. As printed the line evaluates to 43, so the swap you want has to remove 16 from the total.

Then test the options rather than solving blind. Four swaps are four short BODMAS runs, and the first one that lands on 27 ends the question.

Key facts

• As printed, 48 ÷ 3 + 12 × 4 – 6 × 7 + 21 evaluates to 43.
• With 3 and 4 interchanged the line reads 48 ÷ 4 + 12 × 3 – 6 × 7 + 21, which evaluates to 27.
• BODMAS settles this line: the division and both multiplications resolve before any addition or subtraction.

Common traps

• Swapping the digits 3 and 4 inside larger numbers instead of the standalone terms
• Working left to right instead of applying BODMAS, which gives a different value for the same line
• Stopping at the first option that moves the total towards 27 without checking it lands on 27

No directly related past PYQ was found.