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

\(18 + (12 × 6) + (63 ÷ 7) × 4 +{(27)^{\frac{1}{3}}}-11=112\:\)

Given :

\(18 + (12 × 6) + (63 ÷ 7) × 4 +{(27)^{\frac{1}{3}}}-11=112\:\)

Calculation:

By option Method:

Option 1 : exchange 18, 11

⇒ \(11 + (12 × 6) + (63 ÷ 7) × 4 +{(27)^{\frac{1}{3}}}-18=112\:\)

⇒11 + 72 + 9 x 4 + 3 - 18 = 112

⇒ 11 + 72 + 36 +3 -18 = 112

⇒ 104 ≠ 112

This is not correct the equation.

Option 2 : exchange 12, 4

⇒ \(18 + (4 × 6) + (63 ÷ 7) × 12 +{(27)^{\frac{1}{3}}}-11=112\:\)

⇒ 18 + 24 + 9 x 12 + 3 -11 = 112

⇒ 18 + 24 + 108 + 3 -11 = 112

⇒ 142 ≠ 112

This is not correct the equation.

Option 3: exchange 6, 4

⇒ \(18 + (12 × 4) + (63 ÷ 7) × 6 +{(27)^{\frac{1}{3}}}-11=112\:\)

⇒ 18 + 48 + 9 x 6 + 3 -11 = 112

⇒ 18 + 48 + 54 + 3 -11 = 112

⇒ 112 = 112

This is correct the equation.

Option 4: exchange 18, 12

⇒ \(12 + (18 × 6) + (63 ÷ 7) × 4 +{(27)^{\frac{1}{3}}}-11=112\:\)

⇒ 12 + 108 + 9 x 4 +3 -11 =112

⇒ 12 + 108 + 36 +3 -11 =112

⇒ 148 ≠ 112

This is not correct the equation.

Hence, 'Option 3' is the correct answer.