Difference between the SI and CI obtained by A and B respectively at ...
Given:
Difference between SI and CI obtained by A and B at a 20% rate of interest per annum for three years is Rs. 768
Both A and B invested the same amount
To find:
Interest obtained by A
Let's assume the principal amount invested by A and B is 'P'.
Simple Interest (SI) formula:
SI = (P * R * T) / 100
Compound Interest (CI) formula:
CI = P * (1 + R/100)^T - P
Where:
P = Principal amount
R = Rate of interest
T = Time period
Since both A and B invested the same amount, the difference between their SI and CI will be due to the difference in the interest earned.
Let's calculate the SI and CI for A and B separately.
For A:
SI(A) = (P * 20 * 3) / 100 = 0.6P
CI(A) = P * (1 + 20/100)^3 - P = P * (1.2)^3 - P = 1.728P - P = 0.728P
For B:
SI(B) = (P * 20 * 3) / 100 = 0.6P
CI(B) = P * (1 + 20/100)^3 - P = P * (1.2)^3 - P = 1.728P - P = 0.728P
Given that the difference between SI and CI obtained by A and B is Rs. 768:
CI(A) - SI(A) = CI(B) - SI(B)
0.728P - 0.6P = 0.728P - 0.6P
0.128P = 0.128P
This implies that the difference between the SI and CI is the same for both A and B, which contradicts the given information. Hence, there seems to be an error in the question.
However, if we assume that the difference between the SI and CI obtained by A and B is Rs. 768, and A's interest is Rs. 768, then we can proceed with the calculation.
0.728P - 0.6P = 768
0.128P = 768
P = 768 / 0.128
P = Rs. 6000
Therefore, the interest obtained by A would be:
SI(A) = (6000 * 20 * 3) / 100 = Rs. 3600
Hence, the correct answer is option 'A' Rs. 3600.
Difference between the SI and CI obtained by A and B respectively at ...
Let the amount invested by A and B beRs.x.
3 x P(R)²/(100)² + P (R/100)³ = 768
3 * x * (20/100)2 + x * (20/100)3 = 768
3 * x * 1/25 + x * 1/125 = 768
15x + x = 125 * 768
16x = 125 * 768
x = Rs.6000
Interest obtained by A = 6000 * 20 * 3/100 = Rs.3600