Multiple choice

A sum of Rs. 1,300 is lent in two parts so that simple interest on the first part for three years at 5% may be equal to simple interest on the second part for 4 years at 6%. Find the sum lent on the first part.

  1. Rs. 800

  2. Rs. 900

  3. Rs. 750

  4. Rs. 589

  5. Rs. 850
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A Correct answer
Explanation

Let the parts be x and 1300-x. Interest 1 = x * 3 * 0.05 = 0.15x. Interest 2 = (1300-x) * 4 * 0.06 = 0.24(1300-x). Setting them equal: 0.15x = 312 - 0.24x, so 0.39x = 312, x = 800.

AI explanation

Let the first part be x, which makes the second part 1300 minus x, and set their simple interests equal using the formula where interest equals principal multiplied by rate multiplied by time divided by 100. This gives the equation x multiplied by 3 multiplied by 5 equals the quantity 1300 minus x multiplied by 4 multiplied by 6. Solving 15x equals 31200 minus 24x results in 39x equaling 31200, so x equals Rs. 800.

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