A certain sum of money amounts to ₹9,766 in 3 years at simple interest at R% per annum and to ₹10,849 in $4\frac{1}{2}$ years at the same rate of simple interest. The value of R is:

9.5

Simple interest of ( 4.5 - 3 ) years = 10849 - 9766 = 1083

Simple interest of 1 year = \(\frac{1083 }{1.5}\) = 722

Simple interest of 3 years = 722 × 3 = 2166

Amount = Principal + Simple Interest

9766 = Principal + 2166

Principal = 7600

We know ,

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

722 = \(\frac{7600 ×R × 1 }{100}\)

R = 9.5%