Question : Directions: Which of the following interchange of mathematical signs would make the given equation correct? 20 ÷ 4 × 8 + 16 – 15 = 11
Option 1: – and ÷
Option 2: + and –
Option 3: × and ÷
Option 4: + and ×
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Correct Answer: × and ÷
Solution : Given: 20 ÷ 4 × 8 + 16 – 15 = 11
Let's check the given options – First option: – and ÷ On interchanging the mathematical signs, we get – ⇒ 20 – 4 × 8 + 16 ÷ 15 = 11 Solving the L.H.S. of the equation – = 20 – 4 × 8 + 16 ÷ 15 = 20 – 4 × 8 + 1.067 = 20 – 32 + 1.067 = 21.067 – 32 = –10.933 ≠ 11 Second option: + and – On interchanging the mathematical signs, we get – ⇒ 20 ÷ 4 × 8 – 16 + 15 = 11 Solving the L.H.S. of the equation – = 20 ÷ 4 × 8 – 16 + 15 = 5 × 8 – 16 + 15 = 40 – 16 + 15 = 55 – 16 = 39 ≠ 11 Third option: × and ÷ On interchanging the mathematical signs, we get – ⇒ 20 × 4 ÷ 8 + 16 – 15 = 11 Solving the L.H.S. of the equation – = 20 × 4 ÷ 8 + 16 – 15 = 20 × 0.5 + 16 – 15 = 10 + 16 – 15 = 26 – 15 = 11 Fourth option: + and × On interchanging the mathematical signs, we get – ⇒ 20 ÷ 4 + 8 × 16 – 15 = 11 Solving the L.H.S. of the equation – = 20 ÷ 4 + 8 × 16 – 15 = 5 + 8 × 16 – 15 = 5 + 128 – 15 = 133 – 15 = 118 ≠ 11
So, only the third option satisfies the given equation. Hence, the third option is correct.
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