Multiple choice

Wasim borrowed some money at $6\%$ p.a simple interest for the first four years, $8\%$ p.a. for the next three years and $10\%$ p.a for a period beyond $7$ years. At the end of $12$ years, he earned Rs$5880$ as simple interest. How much money did he borrow?

  1. Rs. $6000$
  2. Rs. $8000$
  3. Rs. $9000$
  4. Rs. $10000$
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A Correct answer
Explanation

Let P be the principal. Interest = (P * 6 * 4 / 100) + (P * 8 * 3 / 100) + (P * 10 * 5 / 100) = 5880. This simplifies to (0.24 + 0.24 + 0.50)P = 5880, so 0.98P = 5880, P = 6000.

AI explanation

Using the formula for simple interest, SI = (P * R * T) / 100, the total interest for the 12-year period is the sum of the interests for the individual periods. This gives us the equation 5880 = P * [(6*4)/100 + (8*3)/100 + (10*5)/100], which simplifies to 5880 = P * [(24 + 24 + 50)/100]. Solving 5880 = 0.98P gives P = 5880 / 0.98, so the money borrowed was Rs. 6000.

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