A person invested a sum of ₹18,600 at x% p.a. and another sum that is twice the former at (x + 2) % p.a., both at simple interest. If the total interest earned on both investments for $3\frac{1}{2}$years is ₹23,110.50, then the rate of interest p.a. on the second investment is:

12.5%

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

Amount = Principal + Interest

Principal = Rs. 18600  ,  Time =   \(\frac{7}{2}\) years

\(\frac{ 18600  × R × \(\frac{7}{2}\)   }{100}\) +  \(\frac{ 18600  × ( R + 2) × \(\frac{7}{2}\)   }{100}\)   = 23110.50  

⇒ 1953 R = 23110.50 - 2604

⇒ R = \(\frac{20506.5 }{1953}\)

⇒ R = 10.5%