A sum of ₹x amounts to ₹9,246 in 4 years and to ₹11,298.75 in 7\(\frac{1 }{2 }\) years, at y% p.a. simple interest. The values of x and y are, respectively:

6900 and 8.5

SI of ( 7\(\frac{1 }{2 }\) - 4 ) years = 11298.75 - 9246

SI of \(\frac{7 }{2 }\)  years = 2052.75

Si of 1 year  = 2052.75 × \(\frac{2 }{7 }\) = 586.5

Si of 4 years = 586.5 × 4 = 2346

Initial sum = 9246 - 2346 = 6900

Simple Interest = \(\frac{Principal ×Rate × Time }{100}\)

586.5 = \(\frac{6900 × Rate × 1 }{100}\)

Rate = 8.5 %

So , Initial sum = 6900 and rate = 8.5%