The simple interest on a sum of money is \(\frac{9 }{35}\) of the sum. If the number of years is numerically \(\frac{5 }{7}\) times of rate percent per annum, then the rate percent per annum is:

6%

Say, Sum = 35

S.I. =  9

Time = \(\frac{5}{7}\) x rate 

⇒ 9 = \(\frac{35\;x\;5R\;x\;R}{7\;x\;100}\)

⇒ 9 = \(\frac{25R^2}{100}\)

⇒ Rate = \(\sqrt {36}\) = 6%