Question
Divide Rs. 2,440 into two parts such that the first part
after 10 years is equal to the second part after 8 years, compound interest being 20% 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+(20/100))10 The second part after 8 years, = y (1+(20/100))8 As given in the problem these two amounts are equal. So, y (1+(20/100))8 = x (1+(20/100))10 Or y/x = (1+(20/100))2 Or y/x = 36/25 We have the x + y = Rs. 2,440 Using the ratio formula, y = 36/(36+25) × 2,440 = Rs. 1,440 x = 25/(36+25) × 2,440 = Rs. 1,000 Alternate method: y/x = (1+20/100)(difference between time) Or y/x = (1+20/100)(10-8) Or y/x = (1+20/100)2 Or y/x = (6/5)2 Or y/x = 36/25 We have the x + y = Rs. 2,440 Using the ratio formula, y = 36/(36+25) × 2,440 = Rs. 1,440 x = 25/(36+25) × 2,440 = Rs. 1,000
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