In the equation 18 x 3 - 2 / 4 + 7 = 59, by interchanging which two numbers can the equation be made correct?

To make the given equation correct, we need to interchange two numbers.
The original equation is:

$$18 \times 3 - 2 \div 4 + 7 = 59$$

First, let's evaluate the Left Hand Side (LHS) of the original equation using the order of operations (multiplication and division before addition and subtraction):

$$18 \times 3 - 2 \div 4 + 7$$ $$= 54 - 0.5 + 7$$ $$= 53.5 + 7$$ $$= 60.5$$

Since $60.5 \neq 59$, the original equation is incorrect. We need to find which interchange makes it correct.

Let's test each option:

• Option 1: Interchange 7 and 3 The equation becomes:

  $$18 \times 7 - 2 \div 4 + 3 = 59$$

  Evaluate LHS:

  $$18 \times 7 - 2 \div 4 + 3$$ $$= 126 - 0.5 + 3$$ $$= 125.5 + 3$$ $$= 128.5$$

  Since $128.5 \neq 59$, this option is incorrect.

• Option 2: Interchange 18 and 4 The equation becomes:

  $$4 \times 3 - 2 \div 18 + 7 = 59$$

  Evaluate LHS:

  $$4 \times 3 - 2 \div 18 + 7$$ $$= 12 - \frac{1}{9} + 7$$ $$= 12 - 0.111... + 7$$ $$= 11.888... + 7$$ $$= 18.888...$$

  Since $18.888... \neq 59$, this option is incorrect.

• Option 3: Interchange 3 and 2 The equation becomes:

  $$18 \times 2 - 3 \div 4 + 7 = 59$$

  Evaluate LHS:

  $$18 \times 2 - 3 \div 4 + 7$$ $$= 36 - 0.75 + 7$$ $$= 35.25 + 7$$ $$= 42.25$$

  Since $42.25 \neq 59$, this option is incorrect.

• Option 4: Interchange 2 and 4 The equation becomes:

  $$18 \times 3 - 4 \div 2 + 7 = 59$$

  Evaluate LHS:

  $$18 \times 3 - 4 \div 2 + 7$$ $$= 54 - 2 + 7$$ $$= 52 + 7$$ $$= 59$$

  Since $59 = 59$, this option makes the equation correct.

The final answer is $\text{2 এবং 4}$