Multiple choice

If the simple interest on a certain sum for 15 months at $7\, \displaystyle \frac{1}{2}$% per annum exceeds the simple interest on the same sum for 8 months at $12\, \displaystyle \frac{1}{2}$% per annum by Rs.32.50, then the sum (in Rs.) is

  1. Rs. 3000

  2. Rs. 3060

  3. Rs. 3120

  4. Rs. 3250
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The first interest equals 9.375% of the principal, while the second equals 8.333% of the principal. Their difference is 1.041667% of the principal, so 0.01041667P = 32.50, giving P = 3120 rupees.

AI explanation

Converting the months to years gives time periods of 1.25 years and 0.66 years. Using the Simple Interest formula, the equation is Principal times 7.5 times 1.25 divided by 100 minus Principal times 12.5 times 0.66 divided by 100 equals 32.50. This simplifies to 0.0625 times Principal, so Principal equals 32.50 divided by 0.0625, which is exactly Rs. 3120.

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