The BODMAS rule is as follows:
Given equation: (42 × 13) + (6 × 4) – (39 ÷ 3) = 105
Let's check each option one by one.
Option 1) 42 and 39, + and −
Given: (42 × 13) + (6 × 4) – (39 ÷ 3) = 105
After interchanging the numbers and signs we get:
⇒ (39 × 13) – (6 × 4) + (42 ÷ 3) = 105
⇒ 507 – 24 + 14 = 105
⇒ 483 + 14 = 105
⇒ 497 ≠ 105
LHS ≠ RHS
Option 2) 42 and 6, + and −
Given: (42 × 13) + (6 × 4) – (39 ÷ 3) = 105
After interchanging the numbers and signs we get:
⇒ (6 × 13) – (42 × 4) + (39 ÷ 3) = 105
⇒ 78 – 168 + 13 = 105
⇒ -90 + 13 = 105
⇒ -77 ≠ 105
LHS ≠ RHS
Option 3) 13 and 3, + and −
Given: (42 × 13) + (6 × 4) – (39 ÷ 3) = 105
After interchanging the numbers and signs we get:
⇒ (42 × 3) – (6 × 4) + (39 ÷ 13) = 105
⇒ 126 – 24 + 3 = 105
⇒ 102 + 3 = 105
⇒ 105 = 105
LHS = RHS
This option makes the equation correct.
Option 4) 13 and 4, ÷ and −
Given: (42 × 13) + (6 × 4) – (39 ÷ 3) = 105
After interchanging the numbers and signs we get:
⇒ (42 × 4) + (6 − 39 ÷ 13) = 105
⇒ 168 + (6 - 3) = 105
⇒ 168 + 3 = 105
⇒ 171 ≠ 105
LHS ≠ RHS
Hence, the correct answer is "Option 3".