Question : Directions: Which of the following interchange of numbers and mathematical signs would make the given equation correct? 72 ÷ 8 × 9 − 36 + 20 = 80
Option 1: 20 and 80, × and +
Option 2: 9 and 36, × and ÷
Option 3: 36 and 72, ÷ and −
Option 4: 8 and 9, + and −
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Correct Answer: 8 and 9, + and −
Solution : Given: 72 ÷ 8 × 9 − 36 + 20 = 80
Let's check the given options – First option: 20 and 80, × and + On interchanging the signs and numbers, we get – ⇒ 72 ÷ 8 + 9 − 36 × 80 = 20 Solving the L.H.S. of the equation – = 72 ÷ 8 + 9 − 36 × 80 = 9 + 9 − 36 × 80 = 9 + 9 − 2880 = 18 − 2880 = −2862 ≠ 20 Second option: 9 and 36, × and ÷ On interchanging the signs and numbers, we get – ⇒ 72 × 8 ÷ 36 − 9 + 20 = 80 Solving the L.H.S. of the equation – = 72 × 8 ÷ 36 − 9 + 20 = 16 − 9 + 20 = 36 – 9 = 27 ≠ 80 Third option: 36 and 72, ÷ and − ⇒ 36 – 8 × 9 ÷ 72 + 20 = 80 Solving the L.H.S. of the equation – = 36 – 8 × 9 ÷ 72 + 20 = 36 – 8 × 0.125 + 20 = 36 – 1 + 20 = 56 – 1 = 55 ≠ 80 Fourth option: 8 and 9, + and − ⇒ 72 ÷ 9 × 8 + 36 – 20 = 80 Solving the L.H.S. of the equation – = 72 ÷ 9 × 8 + 36 – 20 = 8 × 8 + 36 – 20 = 64 + 36 – 20 = 100 – 20 = 80
So, only the fourth option satisfies the given equation. Hence, the fourth option is correct.
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