Question : Directions: Which two numbers, from amongst the given options, should be interchanged to make the given equation correct? 72 + (7 × 8) – (126 ÷ 14) – (4)2 = 150
Option 1: 72 and 126
Option 2: 7 and 4
Option 3: 8 and 4
Option 4: 14 and 7
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Correct Answer: 14 and 7
Solution : Given: 72 + (7 × 8) – (126 ÷ 14) – (4) 2 = 150
Let's check the options – First option: 72 and 126 On interchanging the numbers, we get – ⇒ 126 + (7 × 8) – (72 ÷ 14) – (4) 2 = 150 Solving the L.H.S. of the equation – = 126 + (7 × 8) – (72 ÷ 14) – (4) 2 = 126 + 56 – 5.14 – 16 = 182 – 5.14 – 16 = 160.86 ≠ 150 Second option: 7 and 4 On interchanging the numbers, we get – ⇒ 72 + (4 × 8) – (126 ÷ 14) – (7) 2 = 150 Solving the L.H.S. of the equation – = 72 + (4 × 8) – (126 ÷ 14) – (7) 2 = 72 + 32 – 9 – 49 = 104 – 9 – 49 = 46 ≠ 150 Third option: 8 and 4 On interchanging the numbers, we get – ⇒ 72 + (7 × 4) – (126 ÷ 14) – (8) 2 = 150 Solving the L.H.S. of the equation – = 72 + (7 × 4) – (126 ÷ 14) – (8) 2 = 72 + 28 – 9 – 64 = 100 – 9 – 64 = 27 ≠ 150 Fourth option: 14 and 7 On interchanging the numbers, we get – ⇒ 72 + (14 × 8) – (126 ÷ 7) – (4) 2 = 150 Solving the L.H.S. of the equation – = 72 + (14 × 8) – (126 ÷ 7) – (4) 2 = 72 + 112 – 18 – 16 = 184 – 18 – 16 = 150
So, only the fourth equation satisfies the given equation. Hence, the fourth option is correct.
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