Multiple choice

Divide Rs 2000 into two sums such that, if the first be put out at simple interest for 6 years at $\displaystyle 3\frac{1}{2}$ per cent and the second for 3 years at $\displaystyle 4\frac{1}{2}$ per cent, the interest on the first sum shall be double that of the second.

  1. Rs 725 Rs 1275

  2. Rs 1125, Rs 875

  3. Rs 1500, Rs 500

  4. Rs 635, Rs 1365
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the parts be x and 2000-x. Interest 1 = x * 3.5 * 6 / 100 = 0.21x. Interest 2 = (2000-x) * 4.5 * 3 / 100 = 0.135(2000-x). Setting 0.21x = 2 * 0.135(2000-x) gives 0.21x = 0.27(2000-x), so 0.48x = 540, x = 1125.

AI explanation

Let the two parts be x and (2000 - x), where the simple interest on the first part is double the interest on the second. Using the simple interest formula, this condition translates to (x * 6 * 3.5 / 100) = 2 * ((2000 - x) * 3 * 4.5 / 100). Simplifying both sides gives the equation 21x / 100 = 27(2000 - x) / 100. Solving for x results in 48x = 54000, which means x = 1125; subtracting this from the total leaves the second sum as Rs. 875.

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