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What will come in the place of '?' in the following equation, if '+' and '÷' are interchanged and '×' and '-' are interchanged? 27÷14×21+3−4=?
16
10
13
15
13
Apply BODMAS rules strictly after replacing symbols: divide and multiply first, then add and subtract.
Apply BODMAS rules strictly after replacing symbols: divide and multiply first, then add and subtract.
Substitute the symbols
Given the interchanges: '+' becomes '÷', '÷' becomes '+', '×' becomes '-', and '-' becomes '×'. The equation 27 ÷ 14 × 21 + 3 - 4 becomes 27 + 14 - 21 ÷ 3 × 4.
Apply BODMAS rules
First, solve division: 21 ÷ 3 = 7. Equation: 27 + 14 - 7 × 4. Next, solve multiplication: 7 × 4 = 28. Equation: 27 + 14 - 28.
Calculate the final result
Addition: 27 + 14 = 41. Final subtraction: 41 - 28 = 13.
A: 16 is incorrect as the calculation results in 13. B: 10 is incorrect as the calculation results in 13. D: 15 is incorrect as the calculation results in 13.
C is correct because by applying the given symbol interchanges and following the BODMAS rule, the equation 27 + 14 - (21 ÷ 3) * 4 simplifies to 27 + 14 - 28, which equals 13.
Always write down the new equation clearly after swapping symbols to avoid confusion, and remember that division must be performed before subtraction.
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