Multiple choice

Abhijit invested an amount with company X for two years at simple interest rate 15 pcpa. He invested the entire amount obtained from company X after two years with company Y at compound interest rate 12 pcpa for two years. If the amount finally received by him was Rs. 81536, what was the amount (in Rs.) invested by him originally with company X?

  1. 65000

  2. 60000

  3. 56000

  4. 50000

  5. 45000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P be principal. After 2 years SI at 15%: A = P(1 + 0.15*2) = 1.3P. This amount is invested at 12% CI for 2 years: 1.3P * (1.12^2) = 81536. 1.3P * 1.2544 = 81536. 1.63072P = 81536. P = 81536 / 1.63072 = 50000.

AI explanation

Let the original principal be P, and using the simple interest formula the amount after two years is P multiplied by the quantity 1 plus 15 multiplied by 2 divided by 100, which simplifies to 1.3P. Investing this amount at compound interest of 12% for two years gives the final amount as 1.3P multiplied by 1.12 squared, resulting in 1.630272P. Equating this to Rs. 81536 and solving for P gives 81536 divided by 1.630272, which equals Rs. 50000.

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