Which two numbers should be interchanged to make the given equation correct?

17 × 7 + (21 ÷ 3) × 5 – 28 + 34 = 72

(NOTE: Numbers must be interchanged and not the constituent digits e.g. if 2 and 3 are to be interchanged in the equation 43 × 3 + 4 ÷ 2, then interchanged equation is 43 × 2+4 ÷ 3)

The correct answer is 7 and 3.

Let's check the given equation step-by-step by interchanging the numbers 7 and 3.

Original Equation:

$17\times 7+(21÷3)\times 5–28+34=72$

After replacing 7 with 3 and 3 with 7, the equation becomes:

$17\times 3+(21÷7)\times 5–28+34$

Now, follow the BODMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction):

Step 1: Solve the division inside the bracket

$21÷7=3$

Substituting this back into the expression:

$17\times 3+3\times 5–28+34$

Step 2: Perform the multiplications

$17\times 3=51$

$3\times 5=15$

Substituting these values back into the equation:

$51+15–28+34$

Step 3: Perform addition and subtraction from left to right

$51+15=66$

$66–28=38$

$38+34=72$

Since the Left-Hand Side (LHS) equals the Right-Hand Side (RHS) of $72$, interchanging 7 and 3 makes the equation correct.