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Interest Calculation with Multiple Borrowings

MAT 2018 · Mathematical Skills · Medium · Simple Interest

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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?

  1. A.

    3.33%

  2. B.

    5%

  3. C.

    8%

  4. D.

    10%

Answer

B

Explanation

Let original rate = r%r\% p.a. Interest on Rs. 1000 for 1 year = 1000×r×1100=10r\frac{1000 \times r \times 1}{100} = 10r. Second amount = Rs. 500 borrowed for 12−4=812 - 4 = 8 months = 812=23\frac{8}{12} = \frac{2}{3} year. Rate for second amount = 3r%3r\%. Interest on second amount = 500×3r×2/3100=10r\frac{500 \times 3r \times 2/3}{100} = 10r. Total interest = 10r+10r=20r10r + 10r = 20r. Given 20r=100  ⟹  r=5%20r = 100 \implies r = 5\%.

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