Multiple choice

Peter invested an amount of Rs. 12,000 at the rate of 10 % p.a. simple interest and. another amount at the rate of 20 % p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14 % p.a. Find the total amount invested.

  1. $Rs. 20,000$
  2. $Rs.22,000$
  3. $Rs. 24,000$
  4. $Rs. 25,000$
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A Correct answer
Explanation

Let the second amount be x. Total interest = 0.10 * 12000 + 0.20 * x = 0.14 * (12000 + x). 1200 + 0.2x = 1680 + 0.14x -> 0.06x = 480 -> x = 8000. Total amount = 12000 + 8000 = 20000.

AI explanation

Using the mixture and alligation method on the interest rates, 10 percent and 20 percent yield an average of 14 percent, giving a ratio of 6 to 4 for the two amounts. This ratio simplifies to 3 to 2, meaning the Rs. 12,000 invested at 10 percent represents 3 parts of the total. Since 1 part is Rs. 4000, the total amount of 5 parts is Rs. 20,000.

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