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?

Accepted Answer

B. Let original rate = $r\%$ p.a. Interest on Rs. 1000 for 1 year = $\frac{1000 	imes r 	imes 1}{100} = 10r$. Second amount = Rs. 500 borrowed for $12 - 4 = 8$ months = $\frac{8}{12} = \frac{2}{3}$ year. Rate for second amount = $3r\%$. Interest on second amount = $\frac{500 	imes 3r 	imes 2/3}{100} = 10r$. Total interest = $10r + 10r = 20r$. Given $20r = 100 \implies r = 5\%$.

Interest Calculation with Multiple Borrowings

Explanation

Practise this under exam conditions