The logic followed here is :-
By using BODMAS RULE :
Option 1) : 12 + 8 × 9 + (24 ÷ 5 + 8) - 7 = 35
After interchanging the signs × and ÷ and the numbers 12 and 9 the equation is as follows : 9 + 8 ÷ 12 + (24 × 5 + 8) - 7 = 35
⇒ 9 + 8 ÷ 12 + (24 × 5 + 8) - 7 = 35
⇒ 9 + 8 ÷ 12 + (120 + 8) - 7 = 35
⇒ 9 + 8 ÷ 12 + 128 - 7 = 35
⇒ 9 + 0.66 + 128 - 7 = 35
⇒ 137.66 - 7 = 35
⇒ 130.66 ≠ 35
LHS ≠ RHS
Option 2) : 9 × 17 + 5 (24 ÷ 9) - 12 = 46
After interchanging the signs × and ÷ and the numbers 12 and 9 the equation is as follows : 12 ÷ 17 + 5 (24 × 12) - 9 = 46
⇒ 12 ÷ 17 + 5 (24 × 12) - 9 = 46
⇒ 12 ÷ 17 + 5 (288) - 9 = 46
⇒ 12 ÷ 17 + 1440 - 9 = 46
⇒ 0.705 + 1440 - 9 = 46
⇒ 1440.705 - 9 = 46
⇒ 1431.705 ≠ 46
LHS ≠ RHS
Option 3) : 14 ÷ 2 + 10 (12 - 6) × 9 = 37
After interchanging the signs × and ÷ and the numbers 12 and 9 the equation is as follows : 14 × 2 + 10 (9 - 6) ÷ 12 = 37
⇒ 14 × 2 + 10 (9 - 6) ÷ 12 = 37
⇒ 14 × 2 + 10 (3) ÷ 12 = 37
⇒ 14 × 2 + 30 ÷ 12 = 37
⇒ 14 × 2 + 2.5 = 37
⇒ 28 + 2.5 = 37
⇒ 30.5 ≠ 37
LHS ≠ RHS
Option 4) : 10 + 2 ÷ 3 + (24 × 9 + 8) - 12 = 17
After interchanging the signs × and ÷ and the numbers 12 and 9 the equation is as follows : 10 + 2 × 3 + (24 ÷ 12 + 8) - 9 = 17
⇒ 10 + 2 × 3 + (24 ÷ 12 + 8) - 9 = 17
⇒ 10 + 2 × 3 + (2 + 8) - 9 = 17
⇒ 10 + 2 × 3 + 10 - 9 = 17
⇒ 10 + 6 + 10 - 9 = 17
⇒ 26 - 9 = 17
⇒ 17 = 17
LHS = RHS
Hence, the correct answer is "10 + 2 ÷ 3 + (24 × 9 + 8) - 12 = 17".