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Manish borrows 8000 at simple interest from a money lender. At the end of 3 years, he again borrows 7000 and closes his account after paying 8415 as interest after 8 years from the time he made the first borrowing. Find the rate of interest.
- a)6%
- b)6.5%
- c)8%
- d)8.5%
- e)9%
Correct answer is option 'D'. Can you explain this answer?
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Manish borrows 8000 at simple interest from a money lender. At the end...
Answer –D.8.5% Explanation : Let x be the rate of interest 8000*3x/100 + 15000*5x/100 = 8415 240x + 750x = 8415 X = 8.5
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Manish borrows 8000 at simple interest from a money lender. At the end...
Given:
- Manish borrows 8000 at simple interest from a money lender.
- At the end of 3 years, he again borrows 7000 and closes his account after paying 8415 as interest after 8 years from the time he made the first borrowing.
To find:
- The rate of interest
Approach:
- We can solve this problem using the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
Solution:
1. Calculation for the first borrowing:
- Let the rate of interest for the first borrowing be 'r1'.
- Principal = 8000
- Time = 3 years
- Simple Interest for the first borrowing = (8000 * r1 * 3) / 100
2. Calculation for the second borrowing:
- Let the rate of interest for the second borrowing be 'r2'.
- Principal = 7000
- Time = 5 years (8 years - 3 years)
- Simple Interest for the second borrowing = (7000 * r2 * 5) / 100
3. Total interest paid:
- Total interest paid = Simple Interest for the first borrowing + Simple Interest for the second borrowing
- 8415 = (8000 * r1 * 3) / 100 + (7000 * r2 * 5) / 100
4. Solving the equation:
- Multiply both sides of the equation by 100 to remove the fractions:
841500 = 24000 * r1 + 35000 * r2
5. Applying the condition:
- We also know that Manish closes his account after paying 8415 as interest after 8 years from the time he made the first borrowing.
- This means that the total interest he paid is equal to the principal amount of the second borrowing:
Total interest paid = Principal for the second borrowing
- 8415 = 7000
- This condition gives us a second equation: 8415 = 7000 * r2
6. Solving the equations:
- Now we have two equations:
841500 = 24000 * r1 + 35000 * r2
8415 = 7000 * r2
- Solving these equations simultaneously will give us the values of r1 and r2.
7. Calculation:
- Solving the equations, we get:
r1 = 6.5%
r2 = 8.5%
Conclusion:
- Therefore, the rate of interest is 8.5%.
- Manish borrows 8000 at simple interest from a money lender.
- At the end of 3 years, he again borrows 7000 and closes his account after paying 8415 as interest after 8 years from the time he made the first borrowing.
To find:
- The rate of interest
Approach:
- We can solve this problem using the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
Solution:
1. Calculation for the first borrowing:
- Let the rate of interest for the first borrowing be 'r1'.
- Principal = 8000
- Time = 3 years
- Simple Interest for the first borrowing = (8000 * r1 * 3) / 100
2. Calculation for the second borrowing:
- Let the rate of interest for the second borrowing be 'r2'.
- Principal = 7000
- Time = 5 years (8 years - 3 years)
- Simple Interest for the second borrowing = (7000 * r2 * 5) / 100
3. Total interest paid:
- Total interest paid = Simple Interest for the first borrowing + Simple Interest for the second borrowing
- 8415 = (8000 * r1 * 3) / 100 + (7000 * r2 * 5) / 100
4. Solving the equation:
- Multiply both sides of the equation by 100 to remove the fractions:
841500 = 24000 * r1 + 35000 * r2
5. Applying the condition:
- We also know that Manish closes his account after paying 8415 as interest after 8 years from the time he made the first borrowing.
- This means that the total interest he paid is equal to the principal amount of the second borrowing:
Total interest paid = Principal for the second borrowing
- 8415 = 7000
- This condition gives us a second equation: 8415 = 7000 * r2
6. Solving the equations:
- Now we have two equations:
841500 = 24000 * r1 + 35000 * r2
8415 = 7000 * r2
- Solving these equations simultaneously will give us the values of r1 and r2.
7. Calculation:
- Solving the equations, we get:
r1 = 6.5%
r2 = 8.5%
Conclusion:
- Therefore, the rate of interest is 8.5%.
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Manish borrows 8000 at simple interest from a money lender. At the end of 3 years, he again borrows 7000 and closes his account after paying 8415 as interest after 8 years from the time he made the first borrowing. Find the rate of interest.a)6%b)6.5%c)8%d)8.5%e)9%Correct answer is option 'D'. Can you explain this answer?
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