Question
Download Solution PDFWhich of the following interchanges of signs would make the given equation correct?
1000 - 448 + 14 ÷ 15 × 2 = 998
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe logic followed here is :-
By using BODMAS RULE :
Option 1) : + and ÷
Given equation is : 1000 - 448 + 14 ÷ 15 × 2 = 998
After interchanging the two signs the equation is as follows : 1000 - 448 ÷ 14 + 15 × 2 = 998
⇒ 1000 - 448 ÷ 14 + 15 × 2 = 998
⇒ 1000 - 32 + 15 × 2 = 998
⇒ 1000 - 32 + 30 = 998
⇒ 1030 - 32 = 998
⇒ 998 = 998
LHS = RHS
Option 2) : × and ÷
Given equation is : 1000 - 448 + 14 ÷ 15 × 2 = 998
After interchanging the two signs the equation is as follows : 1000 - 448 + 14 × 15 ÷ 2 = 998
⇒ 1000 - 448 + 14 × 15 ÷ 2 = 998
⇒ 1000 - 448 + 14 × 7.5 = 998
⇒ 1000 - 448 + 105 = 998
⇒ 1105 - 448 = 998
⇒ 657 ≠ 998
LHS ≠ RHS
Option 3) : - and +
Given equation is : 1000 - 448 + 14 ÷ 15 × 2 = 998
After interchanging the two signs the equation is as follows : 1000 + 448 - 14 ÷ 15 × 2 = 998
⇒ 1000 + 448 - 14 ÷ 15 × 2 = 998
⇒ 1000 + 448 - 0.933 × 2 = 998
⇒ 1000 + 448 - 1.866 = 998
⇒ 1448 - 1.866 = 998
⇒ 1446.133 ≠ 998
LHS ≠ RHS
Option 4) : ÷ and -
Given equation is : 1000 - 448 + 14 ÷ 15 × 2 = 998
After interchanging the two signs the equation is as follows : 1000 ÷ 448 + 14 - 15 × 2 = 998
⇒ 1000 ÷ 448 + 14 - 15 × 2 = 998
⇒ 2.232 + 14 - 15 × 2 = 998
⇒ 2.232 + 14 - 30 = 998
⇒ 16.232 - 30 = 998
⇒ -13.7678 ≠ 998
LHS ≠ RHS
Hence, the correct answer is "+ and ÷".
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