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The compound interest on a certain sum for 2 years is Rs. 786 and S.I. is Rs. 750. If the sum is invested such that the S.I. is Rs. 1296 and the number of years is equal to the rate per cent per annum, Find the rate of interest?
- a)4%
- b)5%
- c)6%
- d)8%
- e)2%
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 years is Rs. 786 and S.I....
CI for 2 years = Rs. 786
SI for 2 years = Rs. 750
36/360 * 100 = 10%
P for first year = 3600
P*x*x/100 = 1296
x = 6%
Most Upvoted Answer
The compound interest on a certain sum for 2 years is Rs. 786 and S.I....
CI for 2 years = Rs. 786
SI for 2 years = Rs. 750
36/360 * 100 = 10%
P for first year = 3600
P*x*x/100 = 1296
x = 6%
SI for 2 years = Rs. 750
36/360 * 100 = 10%
P for first year = 3600
P*x*x/100 = 1296
x = 6%
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Community Answer
The compound interest on a certain sum for 2 years is Rs. 786 and S.I....
Given:
Compound interest (CI) for 2 years = Rs. 786
Simple interest (SI) = Rs. 750
Formula:
Compound Interest (CI) = P(1 + (r/100))^n - P
where,
P = principal amount
r = rate of interest
n = time in years
Simple Interest (SI) = P * r * n / 100
Calculation:
Let's assume the principal amount is P and the rate of interest is r%.
Case 1:
Compound Interest (CI) for 2 years = Rs. 786
CI = P(1 + (r/100))^2 - P
786 = P(1 + (r/100))^2 - P
Simplifying the equation:
(1 + (r/100))^2 = 786/P + 1
(1 + (r/100))^2 = (786 + P) / P
Taking square root on both sides:
1 + (r/100) = √((786 + P) / P)
r/100 = √((786 + P) / P) - 1
r = 100 * (√((786 + P) / P) - 1) ---- Equation 1
Case 2:
Simple Interest (SI) = Rs. 750
SI = P * r * n / 100
750 = P * r * n / 100
n = 750 * 100 / (P * r)
Since it is given that the number of years is equal to the rate per cent per annum:
n = r
Substituting the value of n in terms of r:
r = 750 * 100 / (P * r)
r^2 = 75000 / P
r = √(75000 / P) ---- Equation 2
Comparison:
From equation 1 and equation 2, we can equate the expressions for r:
100 * (√((786 + P) / P) - 1) = √(75000 / P)
Simplifying the equation:
√((786 + P) / P) - 1 = √(750 / P)
√(786 + P) - √P = √(750)
√(786 + P) - √P = √(750)
Squaring both sides:
786 + P - 2√(786 + P)√P + P = 750
2P - 2√(786 + P)√P = 750 - 786
2P - 2√(786 + P)√P = -36
2√(786 + P)√P - 2P = 36
Dividing both sides by 2:
√(786 + P)√P - P = 18
Adding P to both sides:
√(786 + P)√P = P + 18
Squaring both sides:
(786 + P)P = P^2 + 36P + 324
Expanding the equation:
786P + P^2 = P^2 + 36P + 324
Simplifying the equation:
786
Compound interest (CI) for 2 years = Rs. 786
Simple interest (SI) = Rs. 750
Formula:
Compound Interest (CI) = P(1 + (r/100))^n - P
where,
P = principal amount
r = rate of interest
n = time in years
Simple Interest (SI) = P * r * n / 100
Calculation:
Let's assume the principal amount is P and the rate of interest is r%.
Case 1:
Compound Interest (CI) for 2 years = Rs. 786
CI = P(1 + (r/100))^2 - P
786 = P(1 + (r/100))^2 - P
Simplifying the equation:
(1 + (r/100))^2 = 786/P + 1
(1 + (r/100))^2 = (786 + P) / P
Taking square root on both sides:
1 + (r/100) = √((786 + P) / P)
r/100 = √((786 + P) / P) - 1
r = 100 * (√((786 + P) / P) - 1) ---- Equation 1
Case 2:
Simple Interest (SI) = Rs. 750
SI = P * r * n / 100
750 = P * r * n / 100
n = 750 * 100 / (P * r)
Since it is given that the number of years is equal to the rate per cent per annum:
n = r
Substituting the value of n in terms of r:
r = 750 * 100 / (P * r)
r^2 = 75000 / P
r = √(75000 / P) ---- Equation 2
Comparison:
From equation 1 and equation 2, we can equate the expressions for r:
100 * (√((786 + P) / P) - 1) = √(75000 / P)
Simplifying the equation:
√((786 + P) / P) - 1 = √(750 / P)
√(786 + P) - √P = √(750)
√(786 + P) - √P = √(750)
Squaring both sides:
786 + P - 2√(786 + P)√P + P = 750
2P - 2√(786 + P)√P = 750 - 786
2P - 2√(786 + P)√P = -36
2√(786 + P)√P - 2P = 36
Dividing both sides by 2:
√(786 + P)√P - P = 18
Adding P to both sides:
√(786 + P)√P = P + 18
Squaring both sides:
(786 + P)P = P^2 + 36P + 324
Expanding the equation:
786P + P^2 = P^2 + 36P + 324
Simplifying the equation:
786
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The compound interest on a certain sum for 2 years is Rs. 786 and S.I. is Rs. 750. If the sum is invested such that the S.I. is Rs. 1296 and the number of years is equal to the rate per cent per annum, Find the rate of interest?a)4%b)5%c)6%d)8%e)2%Correct answer is option 'C'. Can you explain this answer?
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The compound interest on a certain sum for 2 years is Rs. 786 and S.I. is Rs. 750. If the sum is invested such that the S.I. is Rs. 1296 and the number of years is equal to the rate per cent per annum, Find the rate of interest?a)4%b)5%c)6%d)8%e)2%Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The compound interest on a certain sum for 2 years is Rs. 786 and S.I. is Rs. 750. If the sum is invested such that the S.I. is Rs. 1296 and the number of years is equal to the rate per cent per annum, Find the rate of interest?a)4%b)5%c)6%d)8%e)2%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The compound interest on a certain sum for 2 years is Rs. 786 and S.I. is Rs. 750. If the sum is invested such that the S.I. is Rs. 1296 and the number of years is equal to the rate per cent per annum, Find the rate of interest?a)4%b)5%c)6%d)8%e)2%Correct answer is option 'C'. Can you explain this answer?.
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