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 $10+30–100\times 50÷25$? (Operations are to be replaced simultaneously)

The correct option is –25.

Let's solve this step-by-step by decoding the mathematical operators according to the rules given in the question.

First, let's list the operator replacements specified by the problem:
1. $+$ means $-$ (Subtraction)
2. $-$ means $\times$ (Multiplication)
3. $\times$ means $÷$ (Division)
4. $÷$ means $+$ (Addition)

Now, we are given the expression:
$10+30-100\times 50÷25$

Replacing the operators simultaneously as defined:
• Replace $+$ with $-$ between 10 and 30.
• Replace $-$ with $\times$ between 30 and 100.
• Replace $\times$ with $÷$ between 100 and 50.
• Replace $÷$ with $+$ between 50 and 25.

This gives us the new expression:
$10-30\times 100÷50+25$

To evaluate this expression correctly, we must follow the BODMAS/PEMDAS rule, which states that division and multiplication are performed first (from left to right), followed by addition and subtraction.

Step 1: Perform the Division
First, evaluate the division part of the expression: $100÷50$

$100÷50=2$

Substituting this back into the expression, we get:
$10-30\times 2+25$

Step 2: Perform the Multiplication
Next, evaluate the multiplication: $30\times 2$

$30\times 2=60$

Substituting this back into the expression:
$10-60+25$

Step 3: Perform Addition and Subtraction
Now we evaluate from left to right:
First, subtract 60 from 10:

$10-60=-50$

Finally, add 25 to the result:

$-50+25=-25$

Thus, the final evaluated value is –25.