(b) 800
Let one number = x
Then, the other number = 4000 – x
Given, 10% of x = 6\(\frac{2}{3}\)% of (4000-x)
\(\Rightarrow\) \(\frac{10}{100}\) x x = \(\frac{20}{3}\) x \(\frac{1}{100}\) x (4000-x)
\(\Rightarrow\) 10x = \(\frac{20}{3}\) x 4000 - \(\frac{20X}{3}\)
\(\Rightarrow\) 10x + \(\frac{20X}{3}\) = \(\frac{20}{3}\) x 4000
\(\Rightarrow\) \(\frac{50X}{3}\) = \(\frac{20}{3}\) x 4000
\(\Rightarrow\) x = \(\frac{20\times4000}{50}\) = 1600
The two numbers are 1600 and 2400.
\(\therefore\) Their difference = 2400 – 1600 = 800.