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What will come in the place of '?' in the following equation, if '÷' and '−' are interchanged and '×' and '+' are interchanged? 16−2+5÷12×2=?
25
18
45
30
30
Apply BODMAS strictly after substituting the operators: '÷' becomes '-', '-' becomes '÷', '+' becomes '×', and '×' becomes '+'.
Apply BODMAS strictly after substituting the operators: '÷' becomes '-', '-' becomes '÷', '+' becomes '×', and '×' becomes '+'.
Operator Substitution
Given interchanged operators: '-' becomes '÷', '÷' becomes '-', '+' becomes '×', '×' becomes '+'. The equation 16 - 2 + 5 ÷ 12 × 2 becomes 16 ÷ 2 × 5 - 12 + 2.
BODMAS Calculation
Following BODMAS: 1. Division: 16 ÷ 2 = 8. 2. Multiplication: 8 × 5 = 40. 3. Addition and Subtraction: 40 - 12 + 2 = 28 + 2 = 30.
A: 25 is incorrect as it results from wrong order of operations. B: 18 is incorrect as it ignores the BODMAS sequence. C: 45 is incorrect due to misapplication of operators.
D is correct because following the rule of BODMAS after operator substitution leads to 16 ÷ 2 × 5 - 12 + 2 = 8 × 5 - 12 + 2 = 40 - 12 + 2 = 30.
Always perform the division and multiplication steps as a single combined unit of processing before addition and subtraction to avoid common errors.
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