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A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is:
  • a)
    10%
  • b)
    11%
  • c)
    12%
  • d)
    121/2%
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
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Solution:

Let the sum be Rs. x and the rate of interest be R% per annum.

Simple Interest for 2 years = 2xR/100 = 2Rx/100

Simple Interest for 3 years = 3xR/100 = 3Rx/100

Compound Interest for 2 years = x(1+R/100)² - x = x[(100+R)²-10000]/10000

Compound Interest for 3 years = x(1+R/100)³ - x = x[(100+R)³-1000000]/1000000

According to the question,

[(x[(100+R)³-1000000]/1000000) - (x[(100+R)²-10000]/10000)] / [(3Rx/100) - (2Rx/100)] = 25/8

Simplifying the above equation, we get

(100+R)² + 100(100+R) / 100 - 10000 / 10000 = 25/8

On solving this equation, we get R = 12.5%

Therefore, the rate of interest per annum is 12.5% (Option D).
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A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is:a)10%b)11%c)12%d)121/2%e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is:a)10%b)11%c)12%d)121/2%e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is:a)10%b)11%c)12%d)121/2%e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is:a)10%b)11%c)12%d)121/2%e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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