A sum of money becomes 3 times in 5 years at simple interest. In how many years will the same sum become 6 times at the same rate of simple interest? / एक धनराशि 5 वर्ष में साधारण ब्याज की दर से तीन गुना हो जाती है। वही धनराशि कितने वर्षों में साधारण ब्याज की दर से स्वयं का 6 गुना हो जायेगा?

For the principal to become 3 times in 5 years at simple interest, the interest earned is 2P. Using SI = P×R×T/100: 2P = P×R×5/100 gives R = 40% per annum. To become 6 times, interest needed is 5P. Solving: 5P = P×40×T/100 gives 5 = 2T/5, so T = 12.5 years. The rate remains constant, and we find the time needed for 5 times the principal as interest.