Question
Divide Rs. 53,285 into two parts such that the amount
received from first part after 12 years is equal to the amount received from second part after 8 years, if interest rate being `12(1)/(2)` % per annum compounded yearly.Solution
Let the first part be x and the second part be y The first part after 12 years = x ( 1 + 25/200 )¹² The second part after 8 years = y ( 1 + 25/200 )⁸ As given in the problem these two amounts are equal. So, y ( 1 + 25/200 )⁸ = x ( 1 + 25/200 )¹² Or y/x = (1 + 25/200 )⁴ Or y/x = 6561/4096 We have the x + y = Rs. 53,285 Using the ratio formula, y = 6561/(6561 + 4096) × 53,285 = Rs. 32,805 x = 4096/(6561 + 4096) × 53,285 = Rs. 20,480
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