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`8,829 is invested into three different sectors in such a way that their amounts at 4%
p.a. S.I. after 5 years; 6 and 8 years are equal. Find each part of the sum.?
p.a. S.I. after 5 years; 6 and 8 years are equal. Find each part of the sum.?
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`8,829 is invested into three different sectors in such a way that the...
Given:
- Total investment amount: $8,829
- Interest rate: 4% per annum
- Time periods: 5 years, 6 years, and 8 years
Let x, y, and z be the amounts invested in the three sectors respectively.
Interest earned after 5 years:
- For the first sector: x * 0.04 * 5 = 0.2x
- For the second sector: y * 0.04 * 5 = 0.2y
- For the third sector: z * 0.04 * 5 = 0.2z
Interest earned after 6 years:
- For the first sector: x * 0.04 * 6 = 0.24x
- For the second sector: y * 0.04 * 6 = 0.24y
- For the third sector: z * 0.04 * 6 = 0.24z
Interest earned after 8 years:
- For the first sector: x * 0.04 * 8 = 0.32x
- For the second sector: y * 0.04 * 8 = 0.32y
- For the third sector: z * 0.04 * 8 = 0.32z
Setting up equations:
- 0.2x = 0.2y
- 0.2y = 0.24y
- 0.2z = 0.32z
Solving the equations:
From the first equation, we get x = y. (1)
From the second equation, we get y = 1.2z. (2)
Substitute (1) into (2):
x = 1.2z
y = 1.2z
x + y + z = $8,829
2.2z = $8,829
z = $4,013.64
From (1):
x = y = $4,013.64
Therefore, the amounts invested in each sector are:
- First sector: $4,013.64
- Second sector: $4,013.64
- Third sector: $4,013.64
This ensures that the amounts in each sector, when invested at 4% per annum for 5, 6, and 8 years, earn the same interest.
- Total investment amount: $8,829
- Interest rate: 4% per annum
- Time periods: 5 years, 6 years, and 8 years
Let x, y, and z be the amounts invested in the three sectors respectively.
Interest earned after 5 years:
- For the first sector: x * 0.04 * 5 = 0.2x
- For the second sector: y * 0.04 * 5 = 0.2y
- For the third sector: z * 0.04 * 5 = 0.2z
Interest earned after 6 years:
- For the first sector: x * 0.04 * 6 = 0.24x
- For the second sector: y * 0.04 * 6 = 0.24y
- For the third sector: z * 0.04 * 6 = 0.24z
Interest earned after 8 years:
- For the first sector: x * 0.04 * 8 = 0.32x
- For the second sector: y * 0.04 * 8 = 0.32y
- For the third sector: z * 0.04 * 8 = 0.32z
Setting up equations:
- 0.2x = 0.2y
- 0.2y = 0.24y
- 0.2z = 0.32z
Solving the equations:
From the first equation, we get x = y. (1)
From the second equation, we get y = 1.2z. (2)
Substitute (1) into (2):
x = 1.2z
y = 1.2z
x + y + z = $8,829
2.2z = $8,829
z = $4,013.64
From (1):
x = y = $4,013.64
Therefore, the amounts invested in each sector are:
- First sector: $4,013.64
- Second sector: $4,013.64
- Third sector: $4,013.64
This ensures that the amounts in each sector, when invested at 4% per annum for 5, 6, and 8 years, earn the same interest.
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`8,829 is invested into three different sectors in such a way that their amounts at 4% p.a. S.I. after 5 years; 6 and 8 years are equal. Find each part of the sum.?
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`8,829 is invested into three different sectors in such a way that their amounts at 4% p.a. S.I. after 5 years; 6 and 8 years are equal. Find each part of the sum.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about `8,829 is invested into three different sectors in such a way that their amounts at 4% p.a. S.I. after 5 years; 6 and 8 years are equal. Find each part of the sum.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for `8,829 is invested into three different sectors in such a way that their amounts at 4% p.a. S.I. after 5 years; 6 and 8 years are equal. Find each part of the sum.?.
`8,829 is invested into three different sectors in such a way that their amounts at 4% p.a. S.I. after 5 years; 6 and 8 years are equal. Find each part of the sum.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about `8,829 is invested into three different sectors in such a way that their amounts at 4% p.a. S.I. after 5 years; 6 and 8 years are equal. Find each part of the sum.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for `8,829 is invested into three different sectors in such a way that their amounts at 4% p.a. S.I. after 5 years; 6 and 8 years are equal. Find each part of the sum.?.
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