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Which two numbers should be interchanged to make the given equation correct? 63тИТ45+14+(81├╖9)├Ч4+18├Ч3=114 (Note: Interchange should be done of the entire number and not individual digits of a given number.)
4 and 3
14 and 18
45 and 81
63 and 81
14 and 18
Test options by substituting the numbers and strictly following BODMAS (Brackets, Division, Multiplication, Addition, Subtraction).
Test options by substituting the numbers and strictly following BODMAS (Brackets, Division, Multiplication, Addition, Subtraction).
Analyze the Equation
The original equation is 63 - 45 + 14 + (81 / 9) * 4 + 18 * 3 = 114. We need to find which pair of numbers when interchanged makes the LHS equal to the RHS (114).
Test Option B (14 and 18)
Interchanging 14 and 18 yields the modified equation: 63 - 45 + 18 + (81 / 9) * 4 + 14 * 3.
Apply BODMAS Rule
First, evaluate the bracket: (81 / 9) = 9. Next, perform multiplication: 9 * 4 = 36 and 14 * 3 = 42. Substitute these back: 63 - 45 + 18 + 36 + 42.
Final Arithmetic Evaluation
Calculate from left to right: 63 - 45 = 18; 18 + 18 = 36; 36 + 36 = 72; 72 + 42 = 114. Since LHS (114) equals RHS (114), Option B is correct.
A: Interchanging 4 and 3 does not yield 114. C: Interchanging 45 and 81 does not yield 114. D: Interchanging 63 and 81 does not yield 114.
B is correct because interchanging 14 and 18 results in 63 - 45 + 18 + (81 / 9) * 4 + 14 * 3, which evaluates to 114 and matches the RHS.
In equation interchange questions, always test division compatibility first to narrow down options where division results in whole numbers.
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