If a + b means a – b; a – b means a × b; a × b means a ÷ b; a ÷ b means a + b, then what is the value of 10 + 30 – 100 × 50 ÷ 25? (Operations are to be replaced simultaneously)

Correct Option (4)

The problem defines a set of new arithmetic operations based on standard symbols:

• 'a + b' is redefined as 'a – b'
• 'a – b' is redefined as 'a × b'
• 'a × b' is redefined as 'a ÷ b'
• 'a ÷ b' is redefined as 'a + b'

The given expression is 10 + 30 – 100 × 50 ÷ 25.

Applying the simultaneous replacement of operations:

The expression transforms into: 10 – 30 × 100 ÷ 50 + 25

To evaluate this new expression, the standard order of operations (BODMAS/PEMDAS) must be followed:

1. Perform division: 100 ÷ 50 = 2

The expression becomes: 10 – 30 × 2 + 25

2. Perform multiplication: 30 × 2 = 60

The expression becomes: 10 – 60 + 25

3. Perform subtraction and addition from left to right:

10 – 60 = –50

–50 + 25 = –25

Thus, the final value of the expression is –25.

Incorrect Options:

Options 1 (15), 2 (0), and 3 (–15) are incorrect. These results would arise from an improper application of the defined operational replacements or a deviation from the established order of arithmetic operations (BODMAS/PEMDAS) during the calculation process.