Divide Rs. 3903 between A and B in such a way that at the rate of compound interest of 4% pr annum, the amount obtained by A after 7 years is equal to the amount obtained by B after 9 years.

Explanation

Let the sum of money given to A be Rs.`x` and that given to B be Rs.`y`.
Then the amount obtained by A after 7 years at the rate of compound interet of 4% per annum
`Rs.x xx(1+4/100)^(7)=Rs.x xx(26/25)^(7)`
Similarly, the amount obtained by B after 9 years at the same rate of interest.
`=Rs. yxx(1+4/100)^(9)`
`impliesRs.yxx(26/25)^(9)`
As per question `x xx(26/25)^(7)=yxx(226/25)^(9)`
`impliesx=yxx(26/25)^(9-7)`
`impliesx=yxx(26/25)^(2)`
`impliesx/y=676/625`
`:.x:y=676:625`
`:.` Sum of money of `A=Rs. 3903xx676/(676+625)`
`=Rs. 3903xx676/1301`
`=Rs. 3xx676=Rs. 2028`
and sum of money of B`=Rs. 3903xx625/(676+625)`
`=Rs. 3903xx625/1301`
`=Rs. 3xx625=Rs. 1875`
Hence the required sum of money is Rs. 2028 obtained by A and the sum of money is Rs. 1875 obtained by B.