Divide ₹66,300 between A and B in such a way that the amount that A receives after 8 years is equal to the amount that B receives after 10 years; with compound interest being compounded annually at a rate of 10% per annum.

A = ₹36,300, B = ₹30,000 

Amount given to A =  A

Amount given to B = ( 66300 - A )

Amount of A after 8 years    = Amount of B after 10 years 

A × ( 1 + \(\frac{rate }{100}\) )8  =   (66300-A) × ( 1 + \(\frac{rate }{100}\) )¹⁰

A × ( 1 + \(\frac{10 }{100}\) )8 =   (66300-A) × ( 1 + \(\frac{10 }{100}\) )¹⁰

A = (66300-A) × ( 1 + \(\frac{10 }{100}\) )^10-8

A = (66300-A) × ( \(\frac{11 }{10}\) )²

100A = 8022300 - 121A

221A = 8022300

A = \(\frac{8022300 }{221}\) = 36300

Amount given to A = 36300

Amount given to B = ( 66300 - 36300 ) = 30000