Quantitative Aptitude Question on Linear Equations in One Variable

Question

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

Answer 1

Solution

Given that
(5.55)x = 1000
(5.55)x = 10³
By Taking log both the side we get
xlog10 ( 5.55 ) = 3
⇒ log10 ( 5.55 ) = $\frac{3}{x}$
⇒ log10 ( 10 × 0.555 ) = $\frac{3}{x}$
⇒ log10 ( 0.555 ) + 1 = $\frac{3}{x}$ ..... (1)
Also, we have
(0.555)y = 1000
Taking log both the side
y log10 ( 0.555 ) = 3
⇒ log10 ( 5.55 ) = $\frac{3}{x}$ ..... (2)
From equation (1) and (2), we get
$\frac{3}{y}+1=\frac{3}{x}$
⇒ $\frac{1}{x}-\frac{1}{y}=\frac{1}{3}$