Question : Directions: Which two numbers from amongst the given options should be interchanged to make the given equation correct? 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77
Option 1: 8 and 4
Option 2: 184 and 77
Option 3: 184 and 248
Option 4: 4 and 6
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Correct Answer: 184 and 248
Solution : Given: 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77
Let's check the options – First option: 8 and 4 ⇒ 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77 Since there are two 4s in the equation, it is unclear which 4 should be interchanged with 8. So, this option is incorrect. Second option: 184 and 77 ⇒ 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77 On interchanging the numbers, the equation becomes – ⇒ 248 ÷ 4 + 77 ÷ (4 × 6 – 2 × 8) = 184 Solving the L.H.S. of the equation – = 248 ÷ 4 + 77 ÷ (4 × 6 – 2 × 8) = 248 ÷ 4 + 77 ÷ (24 – 16) = 248 ÷ 4 + 77 ÷ 8 = 62 + 9.625 = 71.625 ≠ 184 Third option: 184 and 248 ⇒ 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77 On interchanging the numbers, the equation becomes – ⇒ 184 ÷ 4 + 248 ÷ (4 × 6 – 2 × 8) = 77 Solving the L.H.S. of the equation – = 184 ÷ 4 + 248 ÷ (4 × 6 – 2 × 8) = 184 ÷ 4 + 248 ÷ (24 – 16) = 184 ÷ 4 + 248 ÷ 8 = 46 + 31 = 77 Fourth option: 4 and 6 ⇒ 248 ÷ 4 + 184 ÷ (4 × 6 – 2 × 8) = 77 Since there are two 4s in the equation, it is unclear which 4 should be interchanged with 6. So, this option is incorrect.
So, only the third option satisfies the given equation. Hence, the third option is correct.
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