Correct Answer: 10 + 2 ÷ 3 + (24 × 9 + 8) – 12 = 17

Solution : Given:
Interchange × and ÷ and the numbers 12 and 9.

Replace the given symbols and numbers in the options one by one with the original symbols and numbers in the given equation.
First option: 12 + 8 × 9 + (24 ÷ 5 + 8) – 7 = 35
⇒ 9 + 8 ÷ 12 + (24 × 5 + 8) – 7 = 35
= 9 + 0.67 + 128 – 7
= 130.67 ≠ 35
Second option: 9 × 17 + 5 (24 ÷ 9) – 12 = 46
⇒ 12 ÷ 17 + 5 (24 × 12) – 9 = 46
= 0.70 + 5 (288) – 9
= 0.70 + 1440 – 9
= 1440.7 – 9
= 1431.7 ≠ 46
Third option: 14 ÷ 2 + 10 (12 – 6) × 9 = 37
⇒ 14 × 2 + 10 (9 – 6) ÷ 12 = 37
= 28 + 10 (3) ÷ 12
= 28 + 30 ÷ 12
= 28 + 2.5
= 30.5 ≠ 37
Fourth option: 10 + 2 ÷ 3 + (24 × 9 + 8) – 12 = 17
⇒ 10 + 2 × 3 + (24 ÷ 12 + 8) – 9 = 17
= 10 + 6 + (2 + 8) – 9
= 16 + 10 – 9
= 17

Here, only the fourth option satisfies the R.H.S. of the given equation. Hence, the fourth option is correct.