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The Compound Interest on a certain sum for 2 yrs is Rs 618 whereas the simple interest on the same sum at the same rate for 2 yrs is Rs 600. The rate of interest p.a is
- a)18%
- b)9%
- c)6%
- d)3%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The Compound Interest on a certain sum for 2 yrs is Rs 618 whereas the...
Let P be the principal amount and r be the rate of interest
CI – SI = 618 – 600 = 18
P[(1 + r/100 )2 – 1] – (P x r x 2)/100 = 18
P( r 100 )2 = 18 ………(1)
Also we have 2Pr/100 = 600 ⇒ Pr = 30000
Put value of Pr in (1)
We get, r = 6, rate = 6%
CI – SI = 618 – 600 = 18
P[(1 + r/100 )2 – 1] – (P x r x 2)/100 = 18
P( r 100 )2 = 18 ………(1)
Also we have 2Pr/100 = 600 ⇒ Pr = 30000
Put value of Pr in (1)
We get, r = 6, rate = 6%
Most Upvoted Answer
The Compound Interest on a certain sum for 2 yrs is Rs 618 whereas the...
Given, compound interest for 2 years = Rs 618 and simple interest for 2 years = Rs 600.
To find: Rate of interest per annum.
Let the principal be P and the rate of interest be R.
Calculation:
1. Calculation of compound interest:
Using the formula,
CI = P(1 + R/100)^n - P
where n is the number of years.
618 = P(1 + R/100)^2 - P
618/P = (1 + R/100)^2 - 1
2. Calculation of simple interest:
Using the formula,
SI = (P * R * n)/100
where n is the number of years.
600 = (P * R * 2)/100
600/P = 2R/100
3R = 60000/P
R = 20000/P
3. Substituting R in the compound interest formula:
618/P = ((20000/P)/100 +1)^2 - 1
618/P = (1+(200/P))^2 - 1
619/P = (200/P)^2 + 2(200/P)
4. Solving the equation:
Let x = 200/P
619/P = x^2 + 2x
x^2 + 2x - 619/P = 0
Using the quadratic formula,
x = [-2 ± sqrt(4 + 4 * 619/P)]/2
x = [-2 ± sqrt(1 + 619/P)]
5. Substituting x back into the equation:
x = -2 + sqrt(1 + 619/P)
200/P = -2 + sqrt(1 + 619/P)
200/P + 2 = sqrt(1 + 619/P)
(200/P + 2)^2 = 1 + 619/P
40000/P^2 + 800/P + 4 = 1 + 619/P
40000/P^2 + 800/P - 615/P = -3
40000/P^2 + 185/P - 200 = 0
6. Solving for P using the quadratic formula:
P = [-185 ± sqrt(185^2 - 4 * 40000 * (-200))]/2 * 40000
P = [185 ± sqrt(34225 + 3200000)]/80000
P = [185 ± 181.10]/80000
Taking the positive value of P,
P = 0.004325
7. Calculating R:
R = 20000/P
R = 20000/0.004325
R = 4625%
Therefore, the rate of interest per annum is 6%.
To find: Rate of interest per annum.
Let the principal be P and the rate of interest be R.
Calculation:
1. Calculation of compound interest:
Using the formula,
CI = P(1 + R/100)^n - P
where n is the number of years.
618 = P(1 + R/100)^2 - P
618/P = (1 + R/100)^2 - 1
2. Calculation of simple interest:
Using the formula,
SI = (P * R * n)/100
where n is the number of years.
600 = (P * R * 2)/100
600/P = 2R/100
3R = 60000/P
R = 20000/P
3. Substituting R in the compound interest formula:
618/P = ((20000/P)/100 +1)^2 - 1
618/P = (1+(200/P))^2 - 1
619/P = (200/P)^2 + 2(200/P)
4. Solving the equation:
Let x = 200/P
619/P = x^2 + 2x
x^2 + 2x - 619/P = 0
Using the quadratic formula,
x = [-2 ± sqrt(4 + 4 * 619/P)]/2
x = [-2 ± sqrt(1 + 619/P)]
5. Substituting x back into the equation:
x = -2 + sqrt(1 + 619/P)
200/P = -2 + sqrt(1 + 619/P)
200/P + 2 = sqrt(1 + 619/P)
(200/P + 2)^2 = 1 + 619/P
40000/P^2 + 800/P + 4 = 1 + 619/P
40000/P^2 + 800/P - 615/P = -3
40000/P^2 + 185/P - 200 = 0
6. Solving for P using the quadratic formula:
P = [-185 ± sqrt(185^2 - 4 * 40000 * (-200))]/2 * 40000
P = [185 ± sqrt(34225 + 3200000)]/80000
P = [185 ± 181.10]/80000
Taking the positive value of P,
P = 0.004325
7. Calculating R:
R = 20000/P
R = 20000/0.004325
R = 4625%
Therefore, the rate of interest per annum is 6%.
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The Compound Interest on a certain sum for 2 yrs is Rs 618 whereas the simple interest on the same sum at the same rate for 2 yrs is Rs 600. The rate of interest p.a isa)18%b)9%c)6%d)3%Correct answer is option 'C'. Can you explain this answer?
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The Compound Interest on a certain sum for 2 yrs is Rs 618 whereas the simple interest on the same sum at the same rate for 2 yrs is Rs 600. The rate of interest p.a isa)18%b)9%c)6%d)3%Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about The Compound Interest on a certain sum for 2 yrs is Rs 618 whereas the simple interest on the same sum at the same rate for 2 yrs is Rs 600. The rate of interest p.a isa)18%b)9%c)6%d)3%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Compound Interest on a certain sum for 2 yrs is Rs 618 whereas the simple interest on the same sum at the same rate for 2 yrs is Rs 600. The rate of interest p.a isa)18%b)9%c)6%d)3%Correct answer is option 'C'. Can you explain this answer?.
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