CDS 2026 (I) Elementary Mathematics, question 89

Topic: Arithmetic (percentage, ratio, interest, time and work, speed)

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Passage · Q89 to Q90

A person borrows a sum of ₹16,00016,000 on simple interest at the beginning of a year. After 44 months, ₹24,00024,000 more is borrowed at a rate of interest double the previous one. At the end of the year, the total interest on both the loans is ₹48004800.

Q89

What is the initial rate of interest per annum ?

  1. (a) 8%8\%
  2. (b) 10%10\%Correct answer
  3. (c) 12%12\%
  4. (d) 16%16\%

Solution.

Answer: (b) 10%10\%

  1. Let the initial rate be r% per annum.
  2. The first loan runs for 12 months, so its interest is 160r.
  3. The second runs for the remaining 8 months at 2r%, giving interest 24000×(2r/100)×(8/12)=320r24000 \times (2r/100) \times (8/12) = 320r.
  4. Thus 160r+320r=4800160r + 320r = 4800, so r=10r = 10.