Question : Directions: Which two signs and two numbers should be interchanged in the following equation to make it correct? 19 + 27 – 4 ÷ 2 × 3 = 20
Option 1: – and ÷; 4 and 3
Option 2: ÷ and ×; 19 and 27
Option 3: – and +; 27 and 2
Option 4: + and ×; 3 and 2
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Correct Answer: – and ÷; 4 and 3
Solution : Given: 19 + 27 – 4 ÷ 2 × 3 = 20
Let's check each option – First Option: – and ÷; 4 and 3 On interchanging the mathematical signs and numbers, we get – 19 + 27 ÷ 3 – 2 × 4 = 20 On solving the L.H.S. of the equation – = 19 + 27 ÷ 3 – 2 × 4 = 19 + 9 – 2 × 4 = 19 + 9 – 8 = 28 – 8 = 20 Second Option: ÷ and ×; 19 and 27 On interchanging the mathematical signs and numbers, we get – 27 + 19 – 4 × 2 ÷ 3 = 20 On solving the L.H.S. of the equation – = 27 + 19 – 4 × 2 ÷ 3 = 27 + 19 – 4 × 0.67 = 27 + 19 – 2.68 = 43.32 ≠ 20 Third Option: – and +; 27 and 2 On interchanging the mathematical signs and numbers, we get – 19 – 2 + 4 ÷ 27 × 3 = 20 On solving the L.H.S. of the equation – = 19 – 2 + 4 ÷ 27 × 3 = 19 – 2 + 0.148 × 3 = 19 – 2 + 0.444 = 17.444 ≠ 20 Fourth Option: + and ×; 3 and 2 On interchanging the mathematical signs and numbers, we get – 19 × 27 – 4 ÷ 3 + 2 = 20 On solving the L.H.S. of the equation – = 19 × 27 – 4 ÷ 3 + 2 = 19 × 27 – 1.33 + 2 = 513 – 1.33 + 2 = 513.67 ≠ 20
So, only the first option satisfies the equation. Hence, the first option is correct.
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