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Which two signs should be interchanged to make the following equation correct?     (SSC Sub. Ins. 2018)
12 – 8 + 12 × 9 ÷ 3 = 9
  • a)
    + and x
  • b)
    + and ÷
  • c)
    – and x
  • d)
    x and ÷
Correct answer is option 'B'. Can you explain this answer?
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Which two signs should be interchanged to make the following equation ...
Correct answer is B.
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Which two signs should be interchanged to make the following equation ...
Understanding the Equation
To solve the equation, we need to analyze it step by step. The original equation is:
12 – 8 + 12 × 9 ÷ 3 = 9
Order of Operations
According to the order of operations (BODMAS/BIDMAS), we perform multiplication and division before addition and subtraction.
- The original equation evaluates as follows:
- 12 – 8 = 4
- 12 × 9 = 108
- 108 ÷ 3 = 36
- So, the equation becomes: 4 + 36 = 40, which is not equal to 9.
Identifying the Signs to Interchange
Now, let's explore the options by interchanging different signs one by one:
1. Interchanging + and -:
- New equation: 12 + 8 – 12 × 9 ÷ 3
- Calculation: 12 + 8 = 20; 12 × 9 = 108; 108 ÷ 3 = 36; 20 – 36 = -16 (not equal to 9)
2. Interchanging + and ÷:
- New equation: 12 – 8 ÷ 12 × 9 – 3
- Calculation: 8 ÷ 12 = 0.67; 12 – 0.67 × 9 – 3 (still complicated and not equal to 9)
3. Interchanging - and ÷:
- New equation: 12 ÷ 8 + 12 × 9 – 3
- Calculation: 12 ÷ 8 = 1.5; 1.5 + 12 × 9 = 1.5 + 108 – 3 = 106.5 (not equal to 9)
4. Interchanging + and ×:
- New equation: 12 – 8 × 12 + 9 ÷ 3
- Calculation: 12 – 96 + 3 = -81 (not equal to 9)
Correct Interchange
The correct interchange is between the signs + and ÷.
- New equation: 12 – 8 ÷ 12 × 9 + 3
- This results in the correct evaluation equal to 9.
Thus, the answer is option 'B' where we interchange the + and ÷ signs.
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