Correct Answer: 3 and 2

Solution : Given:
12 ÷ 3 − 2 + 5 × 4 = 23

Let's check each option –
First Option: 3 and 4
On interchanging the numbers, we get –
12 ÷ 4 − 2 + 5 × 3 = 23
On solving the L.H.S. of the equation –
= 12 ÷ 4 − 2 + 5 × 3
= 3 − 2 + 5 × 3
= 3 − 2 + 15
= 16 ≠ 23
Second Option: 3 and 2
On interchanging the numbers, we get –
12 ÷ 2 − 3 + 5 × 4 = 23
On solving the L.H.S. of the equation –
= 12 ÷ 2 − 3 + 5 × 4
= 6 − 3 + 5 × 4
= 6 − 3 + 20
= 23
Third Option: 3 and 5
On interchanging the numbers, we get –
12 ÷ 5 − 2 + 3 × 4 = 23
On solving the L.H.S. of the equation –
= 12 ÷ 5 − 2 + 3 × 4
= 2.4 − 2 + 3 × 4
= 2.4 − 2 + 12
= 12.4 ≠ 23
Fourth Option: 4 and 5
On interchanging the numbers, we get –
12 ÷ 3 − 2 + 4 × 5 = 23
On solving the L.H.S. of the equation –
= 12 ÷ 3 − 2 + 4 × 5
= 4 − 2 + 4 × 5
= 4 − 2 + 20
= 22 ≠ 23

So, only the second option satisfies the equation. Hence, the second option is correct.