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 –

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.