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.

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