Question : Directions: Which of the following interchanges of signs would make the given equation correct? 100 + 100 × 50 – 2 ÷ 3 = 51
Option 1: + and ÷
Option 2: + and –
Option 3: – and ×
Option 4: ÷ and ×
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Correct Answer: + and ÷
Solution : Given: 100 + 100 × 50 – 2 ÷ 3 = 51
On interchanging the mathematical signs as directed in the options – First option: + and ÷ ⇒ 100 ÷ 100 × 50 – 2 + 3 = 51 Solving the L.H.S. of the given equation – = 1 × 50 – 2 + 3 = 50 – 2 + 3 = 53 – 2 = 51 = R.H.S. Second option: + and – ⇒ 100 – 100 × 50 + 2 ÷ 3 = 51 Solving the L.H.S. of the given equation – = 100 – 100 × 50 + 0.67 = 51 = 100 – 5000 + 0.67 = 100.67 – 5000 = –4899.33 ≠ 51 Third option: – and × ⇒ 100 + 100 – 50 × 2 ÷ 3 = 51 Solving the L.H.S. of the given equation – = 100 + 100 – 50 × 0.67 = 100 + 100 – 33.5 = 200 – 33.5 = 166.5 ≠ 51 Fourth option: ÷ and × ⇒ 100 + 100 ÷ 50 – 2 × 3 = 51 Solving the L.H.S. of the given equation – = 100 + 2 – 2 × 3 = 100 + 2 – 6 = 102 – 6 = 96 ≠ 51
So, only the first option satisfies the R.H.S. of the given equation. Hence, the first option is correct.
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