Question : Directions: Which of the following interchanges of numbers and mathematical signs would make the given equation correct? 729 × 81 ÷ 20 + 16 − 6 = 50
Option 1: 6 and 20, × and ÷
Option 2: 20 and 50, + and −
Option 3: 16 and 50, × and +
Option 4: 16 and 20, + and ÷
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Correct Answer: 6 and 20, × and ÷
Solution : Given: 729 × 81 ÷ 20 + 16 − 6 = 50
Let's check the given options – First option: 6 and 20, × and ÷ On interchanging the signs and numbers, we get – ⇒ 729 ÷ 81 × 6 + 16 − 20 = 50 Solving the L.H.S. of the equation – = 9 × 6 + 16 − 20 = 54 + 16 − 20 = 70 − 20 = 50 Second option: 20 and 50, + and − On interchanging the signs and numbers, we get – ⇒ 729 × 81 ÷ 50 − 16 + 6 = 20 Solving the L.H.S. of the equation – = 729 × 1.62 − 16 + 6 = 1180.98 − 16 + 6 = 1186.98 – 16 = 1170.98 ≠ 20 Third option: 16 and 50, × and + On interchanging the signs and numbers, we get – ⇒ 729 + 81 ÷ 20 × 50 − 6 = 16 Solving the L.H.S. of the equation – = 729 + 4.05 × 50 − 6 = 729 + 202.50 – 6 = 931.50 – 6 = 925.5 ≠ 16 Fourth option: 16 and 20, + and ÷ On interchanging the signs and numbers, we get – ⇒ 729 × 81 + 16 ÷ 20 − 6 = 50 Solving the L.H.S. of the equation – = 729 × 81 + 0.80 − 6 = 59049 + 0.80 – 6 = 59049.80 – 6 = 59043.80 ≠ 50
So, only the first option satisfies the given equation. Hence, the first option is correct.
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