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The S.I. on a sum of money is 4/9th of the principle and the number of years is equal to the rate percent, find the rate.?
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The S.I. on a sum of money is 4/9th of the principle and the number of...
Understanding the Problem
To solve the problem, we need to analyze the given information regarding Simple Interest (SI), Principal (P), Rate (R), and Time (T).
Given Information
- SI = 4/9 of Principal (P)
- Time (T) = Rate (R)
Formulas Involved
- Simple Interest (SI) is calculated as:
SI = (P * R * T) / 100
- From the problem, we can substitute SI with 4/9 * P:
4/9 * P = (P * R * T) / 100
Setting Up the Equation
- Since T = R, we replace T in the equation:
4/9 * P = (P * R * R) / 100
- Cancelling P from both sides (assuming P is not zero):
4/9 = (R^2) / 100
Solving for Rate (R)
- Rearranging the equation gives:
R^2 = (4/9) * 100
R^2 = 400 / 9
- Taking the square root of both sides:
R = √(400 / 9)
R = 20 / 3
- Converting to percentage:
R = 6.67%
Conclusion
The rate of interest is approximately 6.67%. This indicates that for every 100 units of currency, the interest earned per year would be about 6.67 units.
This method clearly illustrates the relationship between simple interest, principal, rate, and time, and provides a systematic approach to solving the problem.
To solve the problem, we need to analyze the given information regarding Simple Interest (SI), Principal (P), Rate (R), and Time (T).
Given Information
- SI = 4/9 of Principal (P)
- Time (T) = Rate (R)
Formulas Involved
- Simple Interest (SI) is calculated as:
SI = (P * R * T) / 100
- From the problem, we can substitute SI with 4/9 * P:
4/9 * P = (P * R * T) / 100
Setting Up the Equation
- Since T = R, we replace T in the equation:
4/9 * P = (P * R * R) / 100
- Cancelling P from both sides (assuming P is not zero):
4/9 = (R^2) / 100
Solving for Rate (R)
- Rearranging the equation gives:
R^2 = (4/9) * 100
R^2 = 400 / 9
- Taking the square root of both sides:
R = √(400 / 9)
R = 20 / 3
- Converting to percentage:
R = 6.67%
Conclusion
The rate of interest is approximately 6.67%. This indicates that for every 100 units of currency, the interest earned per year would be about 6.67 units.
This method clearly illustrates the relationship between simple interest, principal, rate, and time, and provides a systematic approach to solving the problem.
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The S.I. on a sum of money is 4/9th of the principle and the number of years is equal to the rate percent, find the rate.?
Question Description
The S.I. on a sum of money is 4/9th of the principle and the number of years is equal to the rate percent, find the rate.? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about The S.I. on a sum of money is 4/9th of the principle and the number of years is equal to the rate percent, find the rate.? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The S.I. on a sum of money is 4/9th of the principle and the number of years is equal to the rate percent, find the rate.?.
The S.I. on a sum of money is 4/9th of the principle and the number of years is equal to the rate percent, find the rate.? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about The S.I. on a sum of money is 4/9th of the principle and the number of years is equal to the rate percent, find the rate.? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The S.I. on a sum of money is 4/9th of the principle and the number of years is equal to the rate percent, find the rate.?.
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