Find the difference between the compound interest and the simple interest on an amount of Rs.15000 at 8% per annum for 2 years.
- Rs. 120
- Rs. 108
- Rs. 96
- Rs. 100
Answer [Detailed Solution Below]
Option 3 : Rs. 96
Free
SSC GD Previous Paper 2 [Held On: 13 Feb 2019 Shift 1]_Hindi
100 Questions 100 Marks 90 Mins
Given:
P = 15000, and R = 8%, Time = 2 years
Formula used:
The difference between CI and SI for 2 years = Pr2/1002
Where, P = Principal, r = rate
Calculation:
As we know,
The difference between CI and SI for 2 years = Pr2/1002
The difference between CI and SI for 2 years
⇒ [15000 × 8 × 8]/[100 × 100]
⇒ Rs. 96
∴ The difference between CI and SI for 2 years is Rs. 96.
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C.P - S.I
[p[1-r/100]^n-p ]-[[P*R*N]/100] = 96.
Where,
p=1500, n=2, R=?, C.P and S.I difference is 96.
[15000[1-r/100]^2-15000 ]-[[1500*R*2]/100] = 96 ...[1].
Now, 15000 common in above so take it out,
15000[1[1-r/100]^2 - 1 ]-[[1*R*2]/100] = 96 ...[2].
Take L.C.M. we get,
15000[[100 + R]^2 - 10000 - [200 x R]/10000] = 96 ...[3].
Where [100 + R]^2 is like [a + b]^2 = [a^2 + b^2 + 2*a*b].
[100^2 + R^2 + 2*100*R] = [10000 + R^2 + 200R].
Sub [10000 + R^2 + 200R] in eqn[3] we get,
15000[ [10000 + R^2 + 200R] - 10000 - [200 x R]/10000] = 96.
15000[ [10000 + R^2 + 200R - 10000 - 200R] /10000] = 96.
Now 10000 and 200R is cancelled, remaining.
15000[ R^2 /10000] = 96.
[15000R^2/10000] = 96.
[15R^2/10] = 96.
divide by 5 we get,
[3R^2/2] = 96.
Now keep the R^2 in left hand side and move 3/2 to right side
R^2 = 96[2/3] // 96/3 = 32.
R^2 = 32*2.
R^2 = 64 // square root of 64 is 8.
R = 8%.
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