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.
Answer & explanation
Correct answer: option 4
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