With reference to a number greater than one, the difference between itself and its reciprocal is 25% of the sum of itself and its reciprocal. By how much percent is the fourth power of the number greater than its square?

66.7

Let the no. = x

x - \(\frac{1}{×}\) = \(\frac{25}{100}\) (x + (\(\frac{1}{×}\))

x² - 1 = \(\frac{1}{4}\) (x² + 1 )

4x² - 4 = x² + 1

3x² = 5

⇒ x² = \(\frac{5}{3}\) & x⁴ = \(\frac{25}{9}\)

Required percentage = \(\frac{\frac{25}{9} -\frac{5}{3}}{\frac{5}{3}}\) × 100 = 66.7%