Multiple choice

$A person invested Rs.__________ at the rate of 12.5% simple interest and a Rs.__________ at the rate of 11.11% simple interest. He received yearly interest of Rs 120. But if he had interchanged the amounts invested, he would have received Rs. 128 as interest. How much did he invest at 12.5% simple interest. Then which of the following fills the gap in order.

  1. 2000,3000 B)3000,4000

  2. 1000,1975$
  3. Only A

  4. Only B

  5. Any Two

  6. Any Three

  7. None of these

Reveal answer Fill a bubble to check yourself
G Correct answer
Explanation

Let the amounts be x at 12.5% and y at 11.11% (which equals 1/9). The equations are: 0.125x + (1/9)y = 120 and (1/9)x + 0.125y = 128. Testing option A (2000, 3000): 0.125(2000) + (1/9)(3000) = 250 + 333.33 ≠ 120. Testing option C (1000, 1975): 0.125(1000) + (1/9)(1975) ≈ 125 + 219.44 ≠ 120. None of the given options satisfy both conditions simultaneously. The correct solution requires solving the system of equations, which yields different values.