A sum of ₹ x amounts to ₹8,563.50 in $3\frac{1}{2}$ years and to ₹10,527 in 7 years at y % p.a. simple interest. The value of x and y, respectively, are

6600 and $8\frac{1}{2}$

SI of ( 7 - 3\(\frac{1 }{2 }\) ) years = 10527 - 8563.50

SI of \(\frac{7 }{2 }\)  years = 1963.50

Si of 1 year  = 1963.50 × \(\frac{2 }{7 }\) = 561

Now , Initial sum = 8563.50 - 1963.50  = 6600

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

561 = \(\frac{6600 × Rate × 1 }{100}\)

Rate = 8.5 %

So , Initial sum = 6600 and Rate = 8.5%