Question

If \[ \left( \frac{0.007}{0.049} + \frac{0.049}{0.007} \right)^2 = \frac{2500}{K - 1}, \text{then the value of } k \text{ is:} \]

• A. 50
• B. 49
• C. 24
• D. 0.07

Hint:

When solving equations with fractions, simplify the terms step-by-step and avoid skipping steps for clarity.

Answer 1

The Correct Option is A

We are given the equation: \[ \left( \frac{0.007}{0.049} + \frac{0.049}{0.007} \right)^2 = \frac{2500}{K - 1}. \] Step 1: First, simplify the expression inside the brackets: \[ \frac{0.007}{0.049} = \frac{7}{49} = \frac{1}{7}, \quad \frac{0.049}{0.007} = \frac{49}{7} = 7. \] So, \[ \frac{1}{7} + 7 = \frac{1}{7} + \frac{49}{7} = \frac{50}{7}. \] Step 2: Now, square the result: \[ \left( \frac{50}{7} \right)^2 = \frac{2500}{49}. \] Step 3: Substitute this into the equation: \[ \frac{2500}{49} = \frac{2500}{K - 1}. \] By cross-multiplying: \[ 49(K - 1) = 2500. \] \[ K - 1 = \frac{2500}{49}. \] Step 4: Simplify the right-hand side: \[ K - 1 = 51. \] Step 5: Finally, solve for \( k \): \[ K = 52. \] Thus, the value of \( k \) is \( 50 \).