Multiple choice

The simple interest on a certain sum at 5% for 9 months is Rs. 10 greater than the simple interest on the same sum at the rate of 3% for 14 months. X = What is the sum of interest in both the cases (i.e. total sum of interest)? Y = 200

  1. X > Y

  2. X < Y

  3. X = Y

  4. None of these

  5. Cannot be determined
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AI explanation

Let the principal be P; using the simple interest formula, the difference in interests is (P multiplied by 5 multiplied by 9) divided by (100 multiplied by 12) minus (P multiplied by 3 multiplied by 14) divided by (100 multiplied by 12) equals 10. This simplifies to 45P divided by 1200 minus 42P divided by 1200 equals 10, so 3P divided by 1200 equals 10, which gives P equals 4000. The interest for the first case is (4000 multiplied by 5 multiplied by 9) divided by 1200, equaling Rs. 150, and the interest for the second case is (4000 multiplied by 3 multiplied by 14) divided by 1200, equaling Rs. 140, making the total sum of interest X equal to Rs. 290, which is greater than Y.

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