Given: 4 × 3 ÷ 6 + 2 – 8 = 10 + 2 × 3 ÷ 5 – 18
According to the question, if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged:
Option 1) 4 and 6; ÷ and ×
4 × 3 ÷ 6 + 2 – 8 = 10 + 2 × 3 ÷ 5 – 18 ⇒ 6 × 3 ÷ 4 + 2 – 8 = 10 + 2 ÷ 3 × 5 – 18
⇒ 6 × 3 ÷ 4 + 2 – 8 = 10 + 2 ÷ 3 × 5 – 18
⇒ 6 × 0.75 + 2 – 8 = 10 + 0.67 × 5 – 18
⇒ 4.5 + 2 – 8 = 10 + 3.35 – 18
⇒ 6.5 - 8 = 13.35 - 18
⇒ -1.5 ≠ -4.65 (LHS ≠ RHS)
Option 2) 2 and 4; + and ×
4 × 3 ÷ 6 + 2 – 8 = 10 + 2 × 3 ÷ 5 – 18 ⇒ 2 × 3 ÷ 6 + 4 – 8 = 10 × 2 + 3 ÷ 5 – 18
⇒ 2 × 3 ÷ 6 + 4 – 8 = 10 × 2 + 3 ÷ 5 – 18
⇒ 2 × 2 + 4 – 8 = 10 × 2 + 0.6 – 18
⇒ 4 + 4 – 8 = 20 + 0.6 – 18
⇒ 8 – 8 = 20.06 – 18
⇒ 0 ≠ 2.06 (LHS ≠ RHS)
Option 3) 6 and 8; + and -
4 × 3 ÷ 6 + 2 – 8 = 10 + 2 × 3 ÷ 5 – 18 ⇒ 4 × 3 ÷ 8 + 2 – 6 = 10 - 2 × 3 ÷ 5 + 18
⇒ 4 × 3 ÷ 8 + 2 – 6 = 10 - 2 × 3 ÷ 5 + 18
⇒ 4 × 0.375 + 2 – 6 = 10 - 2 × 0.6 + 18
⇒ 1.5 + 2 – 6 = 10 + 18 - 1.2
⇒ 3.5 – 6 = 28 - 1.2
⇒ -2.5 ≠ 26.8 (LHS ≠ RHS)
Option 4) 4 and 8; + and ÷
4 × 3 ÷ 6 + 2 – 8 = 10 + 2 × 3 ÷ 5 – 18 ⇒ 8 × 3 ÷ 6 + 2 – 4 = 10 ÷ 2 × 3 + 5 – 18
⇒ 8 × 3 ÷ 6 + 2 – 4 = 10 ÷ 2 × 3 + 5 – 18
⇒ 8 × 0.5 + 2 – 4 = 5 × 3 + 5 – 18
⇒ 4 + 2 – 4 = 15 + 5 – 18
⇒ 6 – 4 = 20 – 18
⇒ 2 = 2 (LHS = RHS)
Hence, "Option 4" is the correct answer.