Which two numbers, from amongst the given options, should be interchanged to make the given equation correct?

14 + 39 - ( \(\sqrt{144}\) ÷  4 ) + ( 5 × 3 ) - 6 = 63

The pattern followed here is:

We have to interchange the given numbers in the options and find which option is correct.

Given: 14 + 39 - ( \(\sqrt{144}\) ÷  4 ) + ( 5 × 3 ) - 6 = 63

Let's check each option one by one:

Option 1) 14 and 6

After interchanging the numbers we get the:

⇒ 6 + 39 - ( \(\sqrt{144}\) ÷  4 ) + ( 5 × 3 ) - 14 = 63

⇒ 6 + 39 - (12 ÷ 4) + (5 × 3) - 14 = 63

⇒ 6 + 39 - 3 + 15 - 14 = 63

⇒ 60 - 3 - 14 = 63

⇒ 43 ≠ 63

⇒ LHS ≠ RHS

Option 2) 5 and 39

After interchanging the numbers we get the:

⇒ 14 + 5 - ( \(\sqrt{144}\) ÷  4) + (39 × 3) - 6 = 63

⇒ 14 + 5 - (12 ÷ 4) + (39 × 3) - 6 = 63

⇒ 14 + 5 - 3 + 117 - 6 = 63

⇒ 136 - 3 - 6 = 63

⇒ 127 ≠ 63

⇒ LHS ≠ RHS

Option 3) 4 and 3

After interchanging the numbers we get the:

⇒ 14 + 39 - ( \(\sqrt{144}\) ÷  3) + ( 5 × 4) - 6 = 63

⇒ 14 + 39 - (12 ÷ 3) + (5 × 4) - 6 = 63

⇒ 14 + 39 - 4 + 20 - 6 = 63

⇒ 73 - 4 - 6 = 63

⇒ 63 = 63

⇒ LHS = RHS

Option 4) 4 and 6

After interchanging the numbers we get the:

⇒ 14 + 39 - (\(\sqrt{144}\) ÷  6) + (5 × 3 ) - 4 = 63

⇒ 14 + 39 - (12 ÷ 6) + (5 × 3) - 4 = 63

⇒ 14 + 39 - 2 + 15 - 4 = 63

⇒ 68 - 2 - 4 = 63

⇒ 62 ≠ 63

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 3".