Question
A sum of Rs. 1,000 is borrowed at a certain rate of
interest. After 4 months, Rs 500 is again borrowed, but this time at a rate of interest that is thrice the original rate. At the end of the year, the total interest on both the amounts is Rs. 100. What is the original rate per annum?Solution
Let the original rate of interest be R% per annum. Interest on Rs. 1,000 for 1 year at R% = {1000 x R x 1}/{100} = 10R After 4 months, Rs. 500 is borrowed again. So, second amount is borrowed for remaining 8 months. Rate of interest for second amount = 3R% per annum Interest on Rs. 500 for 8 months at 3R% = {500 x 3R x 8}/{100 x 12} = 10R According to the question, 10R + 10R = 100 20R = 100 R = 5 Therefore, the original rate of interest is 5% per annum.
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