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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. |
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Answer» 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. |
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