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The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest?
Most Upvoted Answer
The ratio of interest between the compound and simple interest after t...
Solution:
Given:
Let the principal be P and the rate of interest be R.
Ratio of compound interest to simple interest after 2 years:
\[
\frac{P((1+\frac{R}{100})^2 - 1)}{P \times \frac{R}{100} \times 2} = \frac{(1+\frac{R}{100})^2 - 1}{\frac{2R}{100}} = \frac{(1+\frac{R}{100})^2 - 1}{\frac{2R}{100}} = 11
\]
Ratio of compound interest to simple interest after 3 years:
\[
\frac{P((1+\frac{R}{100})^3 - 1)}{P \times \frac{R}{100} \times 3} = \frac{(1+\frac{R}{100})^3 - 1}{\frac{3R}{100}} = \frac{(1+\frac{R}{100})^3 - 1}{\frac{3R}{100}} = 37
\]
Solving the ratios:
\[
\frac{(1+\frac{R}{100})^2 - 1}{\frac{2R}{100}} = 11
\]
\[
\frac{(1+\frac{R}{100})^3 - 1}{\frac{3R}{100}} = 37
\]
Solving the above equations will give us the value of R, the rate of interest.
Given:
Let the principal be P and the rate of interest be R.
Ratio of compound interest to simple interest after 2 years:
\[
\frac{P((1+\frac{R}{100})^2 - 1)}{P \times \frac{R}{100} \times 2} = \frac{(1+\frac{R}{100})^2 - 1}{\frac{2R}{100}} = \frac{(1+\frac{R}{100})^2 - 1}{\frac{2R}{100}} = 11
\]
Ratio of compound interest to simple interest after 3 years:
\[
\frac{P((1+\frac{R}{100})^3 - 1)}{P \times \frac{R}{100} \times 3} = \frac{(1+\frac{R}{100})^3 - 1}{\frac{3R}{100}} = \frac{(1+\frac{R}{100})^3 - 1}{\frac{3R}{100}} = 37
\]
Solving the ratios:
\[
\frac{(1+\frac{R}{100})^2 - 1}{\frac{2R}{100}} = 11
\]
\[
\frac{(1+\frac{R}{100})^3 - 1}{\frac{3R}{100}} = 37
\]
Solving the above equations will give us the value of R, the rate of interest.
Community Answer
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The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest?
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The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest?.
The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of interest between the compound and simple interest after two years on a sum of money to that after three years on the same sum, at the same rate of interest, is 11: 37. What will be the rate of interest?.
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