Question : Directions: Which of the following interchange of numbers and signs would make the given equation correct? 10 − 4 ÷ 20 + 16 × 8 = 16
Option 1: 10 and 16, × and ÷
Option 2: 4 and 8, × and −
Option 3: 4 and 20, + and ÷
Option 4: 10 and 20, + and ×
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Correct Answer: 4 and 8, × and −
Solution : Given: 10 − 4 ÷ 20 + 16 × 8 = 16
Let's check the given options – First option: 10 and 16, × and ÷ Since there are two 16s in the equation, it is not clear which 16 needs to be interchanged. So, this option is incorrect. Second option: 4 and 8, × and − On interchanging the signs and numbers, we get – ⇒ 10 × 8 ÷ 20 + 16 – 4 = 16 Solving the L.H.S. of the equation – = 10 × 0.4 + 16 – 4 = 4 + 16 − 4 = 16 Third option: 4 and 20, + and ÷ On interchanging the signs and numbers, we get – ⇒ 10 − 20 + 4 ÷ 16 × 8 = 16 Solving the L.H.S. of the equation – = 10 − 20 + 0.25 × 8 = 10 – 20 + 2 = 12 – 20 = –8 ≠ 16 Fourth option: 10 and 20, + and × On interchanging the signs and numbers, we get – ⇒ 20 − 4 ÷ 10 × 16 + 8 = 16 Solving the L.H.S. of the equation – = 20 − 0.4 × 16 + 8 = 20 − 2.4 + 8 = 28 – 2.4 = 25.6 ≠ 16
So, only the second option satisfies the given equation. Hence, the second option is correct.
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