Which two numbers should be interchanged to make the given equation correct?
$$64 - 17 + 55 \times 65 \div 5 = 230$$

Here we need to check each of the option to get the correct answer.

Option (a) 55 and 65

$$64 - 17 + 65 \times 55 \div 5 = 230$$

$$64 - 17 + 65 \times 11 = 230$$

$$47 +715  = 230$$

$$762\ne\ 230$$

This option is not satisfying the given equation. So this will not be answer.

Option (b) 17 and 55

$$64 - 55 + 17 \times 65 \div 5 = 230$$
$$64 - 55 + 17 \times 13 = 230$$

$$64 - 55 + 221 = 230$$

230 = 230

This option is satisfying the given equation. So this will be answer.

Option (c) 64 and 17

$$17 - 64 + 55 \times 65 \div 5 = 230$$

$$17 - 64 + 55 \times 13 = 230$$

$$17 - 64 + 715 = 230$$

$$668\ne\ 230$$

This option is not satisfying the given equation. So this will not be answer.

Option (d) 17 and 65

$$64 - 65 + 55 \times 17 \div 5 = 230$$

$$64-65+55\times\frac{17}{5}=230$$

$$-1+11\times17=230$$

$$-1+187=230$$

$$186\ne\ 230$$

This option is not satisfying the given equation. So this will not be answer.