Multiple choice

I derive an annual income of Rs 688.25 from Rs 10000 invested partly at 8% p.a, and partly at 5% p.a. simple interest. What is the ratio of my money invested at 5% to the investment at 8%.

  1. $114 : 165$
  2. $51 : 58$
  3. $97 : 113$
  4. $149 : 251$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the amount at 8% and y be the amount at 5%. We have x + y = 10000 and 0.08x + 0.05y = 688.25. Solving this system gives 0.03x = 688.25 - 500 = 188.25, so x = 6275 and y = 3725. The ratio of 5% investment to 8% investment is 3725 : 6275, which simplifies to 149 : 251.

AI explanation

Let the investment at 8% be x and the investment at 5% be (10000 - x). Using the simple interest formula, the total interest equation is 0.08x + 0.05(10000 - x) = 688.25. Simplifying this gives 0.03x + 500 = 688.25, so 0.03x = 188.25 and x = 6275. The ratio of the money invested at 5% to the investment at 8% is (10000 - 6275) to 6275, which is 3725 to 6275; dividing both sides by 25 gives the ratio 149 : 251.

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