Question : Directions: Which two numbers from the given options should be interchanged to make the given equation correct? 54 – (3 × 12) ÷ (8)1/3 + (11 × 4) + 6 = 69
Option 1: 11 and 6
Option 2: 4 and 12
Option 3: 6 and 4
Option 4: 3 and 4
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Correct Answer: 3 and 4
Solution : Given: 54 – (3 × 12) ÷ (8) 1/3 + (11 × 4) + 6 = 69
Let's check the options – First option: 11 and 6 On interchanging the numbers, we get – ⇒ 54 – (3 × 12) ÷ (8) 1/3 + (6 × 4) + 11 = 69 Solving the L.H.S. of the equation – = 54 – (3 × 12) ÷ (8) 1/3 + (6 × 4) + 11 = 54 – 36 ÷ 2 + 24 + 11 = 54 – 18 + 24 + 11 = 89 – 18 = 71 ≠ 69 Second option: 4 and 12 On interchanging the numbers, we get – ⇒ 54 – (3 × 4) ÷ (8) 1/3 + (11 × 12) + 6 = 69 Solving the L.H.S. of the equation – = 54 – (3 × 4) ÷ (8) 1/3 + (11 × 12) + 6 = 54 – 12 ÷ 2 + 132 + 6 = 54 – 6 + 132 + 6 = 192 – 6 = 186 ≠ 69 Third option: 6 and 4 On interchanging the numbers, we get – ⇒ 54 – (3 × 12) ÷ (8) 1/3 + (11 × 6) + 4 = 69 Solving the L.H.S. of the equation – = 54 – (3 × 12) ÷ (8) 1/3 + (11 × 6) + 4 = 54 – 36 ÷ 2 + 66 + 4 = 54 – 18 + 66 + 4 = 124 – 18 = 106 ≠ 69 Fourth option: 3 and 4 On interchanging the numbers, we get – ⇒ 54 – (4 × 12) ÷ (8) 1/3 + (11 × 3) + 6 = 69 Solving the L.H.S. of the equation – = 54 – (4 × 12) ÷ (8) 1/3 + (11 × 3) + 6 = 54 – 48 ÷ 2 + 33 + 6 = 54 – 24 + 33 + 6 = 93 – 24 = 69
So, only the fourth option satisfies the given equation. Hence, the fourth option is correct.
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