Question : Direction: Which of the following interchange of numbers and signs would make the given equation correct? 512 × 64 ÷ 5 + 30 – 50 = 20
Option 1: 50 and 64, + and ×
Option 2: 20 and 30, + and ÷
Option 3: 20 and 50, × and ÷
Option 4: 5 and 20, + and –
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Correct Answer: 20 and 50, × and ÷
Solution : Given: 512 × 64 ÷ 5 + 30 – 50 = 20
Replace the given symbols and numbers in the options one by one with the original symbols and numbers in the given equation.
Let's check the options – First option: 50 and 64, + and × ⇒ 512 + 50 ÷ 5 × 30 – 64 = 20 Solving the L.H.S of the equation – = 512 + 50 ÷ 5 × 30 – 64 = 512 + 10 × 30 – 64 = 512 + 300 – 64 = 812 – 64 = 748 ≠ 20 LHS ≠ RHS Second option: 20 and 30, + and ÷ ⇒ 512 × 64 + 5 ÷ 20 – 50 = 30 Solving the L.H.S of the equation – = 512 × 64 + 5 ÷ 20 – 50 = 512 × 64 + 0.25 – 50 = 32768 + 0.25 – 50 = 32768.25 – 50 = 32718.25 ≠ 30 LHS ≠ RHS Third option: 20 and 50, × and ÷ ⇒ 512 ÷ 64 × 5 + 30 – 20 = 50 Solving the L.H.S of the equation – = 512 ÷ 64 × 5 + 30 – 20 = 8 × 5 + 30 – 20 = 40 + 30 – 20 = 70 – 20 = 50 LHS = RHS Fourth option: 5 and 20, + and – ⇒ 512 × 64 ÷ 20 – 30 + 50 = 5 Solving the L.H.S of the equation – = 512 × 64 ÷ 20 – 30 + 50 = 512 × 3.2 – 30 + 50 = 1638.40 – 30 + 50 = 1688.40 – 30 = 1658.40 ≠ 5 LHS ≠ RHS
So, only the third option satisfies the given equation. Hence, the third option is correct.
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