Multiple choice

A sum of Rs. 2600 is lent in two parts in such a way that the simple interest on one part at 10% for 5 years is equal to that on the other part at 9% (simple interest) for 6 years. The sum that is lent for 5 years at the rate of 10% is

  1. Rs. 1250

  2. Rs. 1350

  3. Rs. 1450

  4. Rs. 1550
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the two parts be x and 2600-x. Simple interest is (P*R*T)/100. Setting (x*10*5)/100 = ((2600-x)*9*6)/100 leads to 50x = 54(2600-x). Solving this gives 50x = 140400 - 54x, so 104x = 140400, x = 1350.

AI explanation

Let the first part be x, which makes the second part 2600 minus x. Using the simple interest formula, the interest on the first part is x multiplied by 10 multiplied by 5 divided by 100, which equals x divided by 2, and the interest on the second part is (2600 minus x) multiplied by 9 multiplied by 6 divided by 100, which equals 1404 minus 0.54x. Setting them equal gives x divided by 2 equals 1404 minus 0.54x, so 1.04x equals 1404, and x equals 1350. The sum lent for 5 years at 10 percent is Rs. 1350.

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