Multiple choice

Ishita 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 her 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 amount at 8%, y at 5%. x+y=10000. 0.08x + 0.05y = 688.25. Solving gives x = 6275, y = 3725. Ratio y:x = 3725:6275 = 149:251.

AI explanation

Using the alligation method, the average interest rate is 688.25 / 10000 = 6.8825%. The differences between the average rate and the two individual rates are 8 - 6.8825 = 1.1175 and 6.8825 - 5 = 1.8825. The ratio of the money invested at 5% to the money invested at 8% is 1.1175 : 1.8825, which simplifies by multiplying by 4000 to get the integer ratio 149 : 251.

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