Question

If (5.55) x (0.555)y = 1000, then the value of 1/x - 1/y is

• A. 3
• B. 1
• C. 1/3
• D. 2/3

Answer 1

The Correct Option is C

We are given: 

\[ (5.55)^x = 1000 \Rightarrow (5.55)^x = 10^3 \]

Step 1: Taking Logarithm on Both Sides

\[ x \log_{10}(5.55) = 3 \Rightarrow \log_{10}(5.55) = \frac{3}{x} \]

Step 2: Expressing 5.55 as a Product

\[ \log_{10}(5.55) = \log_{10}(10 \times 0.555) = \log_{10}(10) + \log_{10}(0.555) = 1 + \log_{10}(0.555) \]

So, \[ \frac{3}{x} = 1 + \log_{10}(0.555) \tag{1} \]

Step 3: Using the Second Given Equation

We are also given: \[ (0.555)^y = 1000 \Rightarrow \log_{10}(0.555) = \frac{3}{y} \tag{2} \]

Step 4: Substituting Equation (2) into Equation (1)

Substitute \(\log_{10}(0.555) = \frac{3}{y}\) into (1): \[ \frac{3}{x} = 1 + \frac{3}{y} \Rightarrow \frac{3}{x} - \frac{3}{y} = 1 \Rightarrow \frac{1}{x} - \frac{1}{y} = \frac{1}{3} \]

Final Answer:

\[ \boxed{ \frac{1}{x} - \frac{1}{y} = \frac{1}{3} } \]