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Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.?
Verified Answer
Mahesh borrowed a certain sum for 2 years at simple interest from Bhim...
We know that SI = PTR/100
P = SI * 100/r*t
= = 400 * 100 / r * 2
= 20000/R ------------------ (1)
We know that CI = P(1+r/100)^n - P
= P(1+r/100)^n - 1
410 = 20000/R(1+r/100)^n - 1
410 = 20000/R(10000 + R^2 + 2000R - 10000)/10000
410 = 2/R(R^2 + 200R)
410R = 2(R^2+200R)
2R^2 + 400R - 410R = 0
2R^2 = 10R
R = 5.
Substitute R in (1), we get
P = 20000/5
= 4000.
Sum = 4000, Rate of interest = 5%.
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Mahesh borrowed a certain sum for 2 years at simple interest from Bhim...
Given Information:
- Mahesh borrowed a certain sum for 2 years at simple interest from Bhim.
- Mahesh lent the same sum to Vishnu for 2 years at a compound interest.
- At the end of 2 years, Mahesh received 410 as compound interest and paid 400 at simple interest.
To Find:
- The sum borrowed by Mahesh.
- The rate of interest.
Assumptions:
- The rate of interest is the same for both the simple interest and compound interest calculations.
Solution:
Let's assume the sum borrowed by Mahesh is 'P' and the rate of interest is 'R'.
Calculating Simple Interest:
Simple interest (SI) is calculated using the formula: SI = (P * R * T) / 100
Given that the simple interest received by Mahesh is 400, we can write the equation as:
400 = (P * R * 2) / 100
Simplifying the equation, we get:
400 * 100 = 2PR
40000 = 2PR -- (Equation 1)
Calculating Compound Interest:
Compound interest (CI) is calculated using the formula: CI = P * (1 + R/100)^T - P
Given that the compound interest received by Mahesh is 410 and the time period is 2 years, we can write the equation as:
410 = P * (1 + R/100)^2 - P
Simplifying the equation, we get:
410 = P * (1 + R/100)^2 - P
410 = P * (1 + 2R/100 + R^2/100^2) - P
410 = P + 2PR/100 + PR^2/100^2 - P
Simplifying further, we get:
410 = 2PR/100 + PR^2/100^2 -- (Equation 2)
Solving the Equations:
From Equation 1, we have:
40000 = 2PR
Solving Equation 2 for P, we get:
410 = 2PR/100 + PR^2/100^2
41000 = 2PR + PR^2/100
41000 = PR(2 + R/100)
41000 = 2PR + PR^2/100
Substituting the value of 2PR from Equation 1 into Equation 2, we get:
41000 = 40000 + PR^2/100
Simplifying further, we get:
PR^2/100 = 1000
R^2 = 100000
R = √100000
R = 100
Substituting the value of R in Equation 1, we get:
40000 = 2P * 100
40000 = 200P
P = 40000/200
P = 200
Conclusion:
- The sum borrowed by Mahesh is 200.
- The rate of interest is 100%.
- Mahesh borrowed a certain sum for 2 years at simple interest from Bhim.
- Mahesh lent the same sum to Vishnu for 2 years at a compound interest.
- At the end of 2 years, Mahesh received 410 as compound interest and paid 400 at simple interest.
To Find:
- The sum borrowed by Mahesh.
- The rate of interest.
Assumptions:
- The rate of interest is the same for both the simple interest and compound interest calculations.
Solution:
Let's assume the sum borrowed by Mahesh is 'P' and the rate of interest is 'R'.
Calculating Simple Interest:
Simple interest (SI) is calculated using the formula: SI = (P * R * T) / 100
Given that the simple interest received by Mahesh is 400, we can write the equation as:
400 = (P * R * 2) / 100
Simplifying the equation, we get:
400 * 100 = 2PR
40000 = 2PR -- (Equation 1)
Calculating Compound Interest:
Compound interest (CI) is calculated using the formula: CI = P * (1 + R/100)^T - P
Given that the compound interest received by Mahesh is 410 and the time period is 2 years, we can write the equation as:
410 = P * (1 + R/100)^2 - P
Simplifying the equation, we get:
410 = P * (1 + R/100)^2 - P
410 = P * (1 + 2R/100 + R^2/100^2) - P
410 = P + 2PR/100 + PR^2/100^2 - P
Simplifying further, we get:
410 = 2PR/100 + PR^2/100^2 -- (Equation 2)
Solving the Equations:
From Equation 1, we have:
40000 = 2PR
Solving Equation 2 for P, we get:
410 = 2PR/100 + PR^2/100^2
41000 = 2PR + PR^2/100
41000 = PR(2 + R/100)
41000 = 2PR + PR^2/100
Substituting the value of 2PR from Equation 1 into Equation 2, we get:
41000 = 40000 + PR^2/100
Simplifying further, we get:
PR^2/100 = 1000
R^2 = 100000
R = √100000
R = 100
Substituting the value of R in Equation 1, we get:
40000 = 2P * 100
40000 = 200P
P = 40000/200
P = 200
Conclusion:
- The sum borrowed by Mahesh is 200.
- The rate of interest is 100%.
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Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.?
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Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.?.
Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.?.
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Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.?, a detailed solution for Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.? has been provided alongside types of Mahesh borrowed a certain sum for 2 years at simple interest from Bhim. Mahesh length is some to Vishnu at the same rate for 2 years at a compound interest. At the end of 2 years Mahesh received 410 as compound interest paid 400 at simple interest.Find the sum and rate of interest.? theory, EduRev gives you an
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