Question : Directions: Which two signs should be interchanged in the given equation to make it mathematically correct? 26 ÷ 24 + 6 × 27 − 105 = 29
Option 1: × and ÷
Option 2: + and ÷
Option 3: + and ×
Option 4: × and −
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Correct Answer: + and ÷
Solution : Given: 26 ÷ 24 + 6 × 27 − 105 = 29
Let's check each option – First Option: × and ÷ On interchanging the mathematical signs, we get – 26 × 24 + 6 ÷ 27 − 105 = 29 On solving the L.H.S. of the equation – = 26 × 24 + 6 ÷ 27 − 105 = 26 × 24 + 0.22 − 105 = 624 + 0.22 − 105 = 519.22 ≠ 29 Second Option: + and ÷ On interchanging the mathematical signs, we get – 26 + 24 ÷ 6 × 27 − 105 = 29 On solving the L.H.S. of the equation – = 26 + 24 ÷ 6 × 27 − 105 = 26 + 4 × 27 − 105 = 26 + 108 − 105 = 29 Third Option: + and × On interchanging the mathematical signs, we get – 26 ÷ 24 × 6 + 27 − 105 = 29 On solving the L.H.S. of the equation – = 26 ÷ 24 × 6 + 27 − 105 = 6.5 + 27 − 105 = –71.5 ≠ 29 Fourth Option: × and – On interchanging the mathematical signs, we get – 26 ÷ 24 + 6 – 27 × 105 = 29 On solving the L.H.S. of the equation – = 26 ÷ 24 + 6 – 27 × 105 = 1.083 + 6 – 27 × 105 = 1.083 + 6 – 2835 = –2827.917 ≠ 29
So, only the second option satisfies the equation. Hence, the second option is correct.
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