Saksham can walk `(2 - 50x^2)` steps to cover (1 - 5x) meters. In how many steps can he cover 1 meter?

Options

A. `2-10x`
B. `2+10x`
C. `2+5x`
D. `2-5x`

Answer

To solve the problem step by step, we will use the information given about Saksham's walking steps and the distance he covers.

### Step 1: Understand the relationship
Saksham can walk \( (2 - 50x^2) \) steps to cover \( (1 - 5x) \) meters. We need to find out how many steps he can take to cover 1 meter.

### Step 2: Set up the equation
Using the unitary method, we can express the number of steps taken to cover 1 meter as:
\[ \text{Steps for 1 meter} = \frac{\text{Total steps}}{\text{Total meters}} = \frac{2 - 50x^2}{1 - 5x} \]

### Step 3: Simplify the expression
Now, we will simplify the expression:
\[ \text{Steps for 1 meter} = \frac{2 - 50x^2}{1 - 5x} \]

### Step 4: Factor the numerator
We notice that the numerator \( 2 - 50x^2 \) can be factored:
\[ 2 - 50x^2 = 2(1 - 25x^2) \]

### Step 5: Recognize the difference of squares
The expression \( 1 - 25x^2 \) can be recognized as a difference of squares:
\[ 1 - 25x^2 = (1 - 5x)(1 + 5x) \]
Thus, we can rewrite the numerator:
\[ 2(1 - 25x^2) = 2(1 - 5x)(1 + 5x) \]

### Step 6: Substitute back into the equation
Now substituting this back into our expression for steps:
\[ \text{Steps for 1 meter} = \frac{2(1 - 5x)(1 + 5x)}{1 - 5x} \]

### Step 7: Cancel out common terms
We can cancel \( (1 - 5x) \) from the numerator and the denominator (as long as \( 1 - 5x \neq 0 \)):
\[ \text{Steps for 1 meter} = 2(1 + 5x) \]

### Step 8: Final expression
Thus, the number of steps Saksham can take to cover 1 meter is:
\[ \text{Steps for 1 meter} = 2 + 10x \]

### Conclusion
The final answer is \( 2 + 10x \).

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