Multiple choice

Mr.Anita Sehgal borrowed some money from a bank at $20\%$ p.a simple interest for $2$ years She invested that money at $20\%$ per annum for $2$ years interest being compound yearly and she gained $Rs\ 800$. Find the money she borrowed from the bank.

  1. $Rs\ 20000$
  2. $Rs\ 13000$
  3. $Rs\ 16000$
  4. $Rs\ 18000$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The simple interest paid is 40% of the borrowed amount, while the yearly compound interest earned is 44%. The gain is therefore 4% of the principal, so 0.04P = 800 and P = Rs. 20000, making option A correct.

AI explanation

Let the sum borrowed be P; the simple interest she owes is (P * 20 * 2) / 100, which equals 0.4P. The compound interest she earns is P * (1 + 20/100)^2 - P, which equals P * (1.44 - 1) = 0.44P. Her gain is the difference between the earned interest and the paid interest, so 0.44P - 0.4P = 800. Solving 0.04P = 800 gives P = 800 / 0.04, meaning the money borrowed was Rs. 20000.

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