Question
Download Solution PDFWhich two signs and two numbers should be interchanged in the following equation to make it correct?
15 ÷ 80 - 34 + 10 × 8 = 102
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe logic followed here is :-
By using BODMAS RULE :
Option 1) : 10, 80, ÷, -
Given equation is : 15 ÷ 80 - 34 + 10 × 8 = 102
After interchanging the two numbers and two signs the equation is as follows : 15 - 10 ÷ 34 + 80 × 8 = 102
⇒ 15 - 10 ÷ 34 + 80 × 8 = 102
⇒ 15 - 0.29411 + 80 × 8 = 102
⇒ 15 - 0.29411 + 640 = 102
⇒ 655 - 0.29411 = 102
⇒ 654.7058 ≠ 102
LHS ≠ RHS
Option 2) : 15, 34, -, ×
Given equation is : 15 ÷ 80 - 34 + 10 × 8 = 102
After interchanging the two numbers and two signs the equation is as follows : 34 ÷ 80 × 15 + 10 - 8 = 102
⇒ 34 ÷ 80 × 15 + 10 - 8 = 102
⇒ 0.425 × 15 + 10 - 8 = 102
⇒ 6.375 + 10 - 8 = 102
⇒ 16.375 - 8 = 102
⇒ 8.375 ≠ 102
LHS ≠ RHS
Option 3) : 34, 15, +, ÷
Given equation is : 15 ÷ 80 - 34 + 10 × 8 = 102
After interchanging the two numbers and two signs the equation is as follows : 34 + 80 - 15 ÷ 10 × 8 = 102
⇒ 34 + 80 - 15 ÷ 10 × 8 = 102
⇒ 34 + 80 - 1.5 × 8 = 102
⇒ 34 + 80 - 12 = 102
⇒ 114 - 12 = 102
⇒ 102 = 102
LHS = RHS
Option 4) : 10, 34, ÷, ×
Given equation is : 15 ÷ 80 - 34 + 10 × 8 = 102
After interchanging the two numbers and two signs the equation is as follows : 15 × 80 - 10 + 34 ÷ 8 = 102
⇒ 15 × 80 - 10 + 34 ÷ 8 = 102
⇒ 15 × 80 - 10 + 4.25 = 102
⇒ 1200 - 10 + 4.25 = 102
⇒ 1204.25 - 10 = 102
⇒ 1194.25 ≠ 102
LHS ≠ RHS
Hence, the correct answer is "34, 15, +, ÷".
Last updated on Jul 14, 2025
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