The SI on a sum is 80% of the principal. The time for which money was lent is \(\frac{4}{5}\) of the numerical value of rate percent per annum. What is the rate percent per annum?

20% 10% 5% 25%

10%

SI = \(\frac{PRT}{100}\)                                 ∵   T = \(\frac{4}{5}\)R 80%P = \(\frac{PR}{100}\) × \(\frac{4R}{5}\) ⇒ \(\frac{80P}{100}\) = \(\frac{P×4R^2}{100×5}\) ⇒  R = 10%