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Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is `9,774. Find the period for which the sum was invested:?
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Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. Wh...
**Given:**
Mr. X invests `90,500 in post office at 7.5% p.a. simple interest.
The rate was wrongly taken as 5.7% p.a.
The difference in amounts at maturity is `9,774.
**To Find:**
The period for which the sum was invested.
**Solution:**
Let's assume the correct rate of interest as r and the period for which the sum was invested as t.
Using the formula for simple interest, we can calculate the correct amount A1 as:
A1 = P(1 + rt)
where, P is the principal amount, r is the rate of interest and t is the time period.
Substituting the given values, we get:
A1 = `90,500(1 + 0.075t)
Similarly, using the wrong rate of interest of 5.7%, we can calculate the wrong amount A2 as:
A2 = `90,500(1 + 0.057t)
The difference between the two amounts is given as `9,774. Therefore,
A1 - A2 = `9,774
`90,500(1 + 0.075t) - `90,500(1 + 0.057t) = `9,774
Simplifying the equation, we get:
0.018t `90,500 = `9,774
t = `9,774 / (0.018 x `90,500)
t = 6.2 years (approx.)
Therefore, the sum was invested for 6.2 years.
**Conclusion:**
The period for which the sum was invested is 6.2 years.
Mr. X invests `90,500 in post office at 7.5% p.a. simple interest.
The rate was wrongly taken as 5.7% p.a.
The difference in amounts at maturity is `9,774.
**To Find:**
The period for which the sum was invested.
**Solution:**
Let's assume the correct rate of interest as r and the period for which the sum was invested as t.
Using the formula for simple interest, we can calculate the correct amount A1 as:
A1 = P(1 + rt)
where, P is the principal amount, r is the rate of interest and t is the time period.
Substituting the given values, we get:
A1 = `90,500(1 + 0.075t)
Similarly, using the wrong rate of interest of 5.7%, we can calculate the wrong amount A2 as:
A2 = `90,500(1 + 0.057t)
The difference between the two amounts is given as `9,774. Therefore,
A1 - A2 = `9,774
`90,500(1 + 0.075t) - `90,500(1 + 0.057t) = `9,774
Simplifying the equation, we get:
0.018t `90,500 = `9,774
t = `9,774 / (0.018 x `90,500)
t = 6.2 years (approx.)
Therefore, the sum was invested for 6.2 years.
**Conclusion:**
The period for which the sum was invested is 6.2 years.
Community Answer
Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. Wh...
90500×7.5×N/100 - 90500×5.7×N/100 = 9774
678750N - 515850N = 977400
162900N = 977400
N = 977400/162900
N = 6 years
678750N - 515850N = 977400
162900N = 977400
N = 977400/162900
N = 6 years
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Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is `9,774. Find the period for which the sum was invested:?
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Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is `9,774. Find the period for which the sum was invested:? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is `9,774. Find the period for which the sum was invested:? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is `9,774. Find the period for which the sum was invested:?.
Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is `9,774. Find the period for which the sum was invested:? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is `9,774. Find the period for which the sum was invested:? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mr. X invests ` 90,500 in post office at 7.5% p.a. simple interest. While calculating the rate was wrongly taken as 5.7% p.a. The difference in amounts at maturity is `9,774. Find the period for which the sum was invested:?.
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