Multiple choice

A sum of $Rs. 2600$ is lent in two parts so that the interest on the first part for a period of $3$ years at $5$% may be equal to the interest on the second part for $6$ years at $4$%. The second part is equal to

  1. $Rs. 1360$
  2. $Rs. 1000$
  3. $Rs. 1440$
  4. $Rs. 720$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let parts be x and 2600-x. Interest: (x * 3 * 5)/100 = ((2600-x) * 6 * 4)/100. 15x = 24(2600-x). 15x = 62400 - 24x. 39x = 62400, x = 1600. Second part = 2600 - 1600 = 1000.

AI explanation

Let the first part be x, so the second part is 2600 minus x. Using the simple interest formula, the interest on the first part is x multiplied by 5 multiplied by 3 divided by 100, and the interest on the second part is 2600 minus x multiplied by 4 multiplied by 6 divided by 100. Setting them equal gives 15 times x equals 24 times 2600 minus x, which simplifies to 39 times x equals 62400. Solving for x gives 1600, making the second part 1000.

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