Multiple choice

Sarita invests a sum of money at a rate of 5% p.a. simple interest and another sum at a rate of 7% p.a. simple interest. Her total interest income after 2 years is Rs. 726. Also, one-third of the first sum is equal to one-fifth of the second sum. Find the total amount invested.

  1. Rs. 5,808

  2. Rs. 5,800

  3. Rs. 5,670

  4. Rs. 5,404

  5. Rs. 5,900
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A Correct answer
Explanation

Let sums be S1 and S2. S1/3 = S2/5 => S2 = 5/3 * S1. Interest: (S1 * 0.05 * 2) + (S2 * 0.07 * 2) = 726. 0.1 * S1 + 0.14 * (5/3 * S1) = 726. 0.1 * S1 + 0.2333 * S1 = 726. 0.3333 * S1 = 726 => S1 = 2178. S2 = 3630. Total = 5808.

AI explanation

Let the first sum be x and the second sum be y; since one-third of the first sum equals one-fifth of the second sum, we have x / 3 = y / 5, which means y equals (5x / 3). The total interest after 2 years is calculated as (x x 5 x 2) / 100 plus (y x 7 x 2) / 100 equals 726. Substituting y gives 0.1x plus 0.14 times (5x / 3) equals 726, which simplifies to 0.1x + 0.233x = 726. Solving for x gives 2178, and using this to find y gives 3630, making the total amount invested 2178 plus 3630, which equals Rs. 5,808.

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