Question
Download Solution PDFWhich of the following interchange of numbers and signs would make the given equation correct?
512 × 64 ÷ 5 + 30 - 50 = 20
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe logic followed here is :-
By using BODMAS RULE :
Option 1) : 50 and 64, + and ×
Given equation is : 512 × 64 ÷ 5 + 30 - 50 = 20
After interchanging the two numbers and two signs the equation is as follows : 512 + 50 ÷ 5 × 30 - 64 = 20
⇒ 512 + 50 ÷ 5 × 30 - 64 = 20
⇒ 512 + 10 × 30 - 64 = 20
⇒ 512 + 300 - 64 = 20
⇒ 812 - 64 = 20
⇒ 748 ≠ 20
Option 2) : 20 and 30, + and ÷
Given equation is : 512 × 64 ÷ 5 + 30 - 50 = 20
After interchanging the two numbers and two signs the equation is as follows : 512 × 64 + 5 ÷ 20 - 50 = 30
⇒ 512 × 64 + 5 ÷ 20 - 50 = 30
⇒ 512 × 64 + 0.25 - 50 = 30
⇒ 32768 + 0.25 - 50 = 30
⇒ 32768.25 - 50 = 30
⇒ 32718.25 ≠ 30
LHS ≠ RHS
Option 3) : 20 and 50, × and ÷
Given equation is : 512 × 64 ÷ 5 + 30 - 50 = 20
After interchanging the two numbers and two signs the equation is as follows : 512 ÷ 64 × 5 + 30 - 20 = 50
⇒ 512 ÷ 64 × 5 + 30 - 20 = 50
⇒ 8 × 5 + 30 - 20 = 50
⇒ 40 + 30 - 20 = 50
⇒ 70 - 20 = 50
⇒ 50 = 50
LHS = RHS
Option 4) : 5 and 20, + and -
Given equation is : 512 × 64 ÷ 5 + 30 - 50 = 20
After interchanging the two numbers and two signs the equation is as follows : 512 × 64 ÷ 20 - 30 + 50 = 5
⇒ 512 × 64 ÷ 20 - 30 + 50 = 5
⇒ 512 × 3.2 - 30 + 50 = 5
⇒ 1638.4 - 30 + 50 = 5
⇒ 1688.4 - 30 = 5
⇒ 1658.4 ≠ 5
LHS ≠ RHS
Hence, the correct answer is "20 and 50, × and ÷ ".
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