What will be the difference between SI and CI on a sum of 15000 for 2 years at the same rate of interest of 12 1 2 per annum?

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%.

S.I. = Rs.  (15000×252×2×1100) =Rs. 3750C.I. = Rs. [15000(1+252×100 )2−15000]=Rs. (15000×98×98−15000)=Rs.  (18948.375−15000)=Rs. 3984.375Difference  = Rs. (3984.375−3750) =Rs. 234.375

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Find the difference between the compound interest and the simple interest on an amount of Rs.15000 at 8% per annum for 2 years.

1. Rs. 120
2. Rs. 108
3. Rs. 96
4. 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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Find the difference between C.I. and S.I. on a sum of Rs. 15000 at 10% for 3 years. 

1. Rs. 440
2. Rs. 465
3. Rs. 455
4. Rs. 485

Answer (Detailed Solution Below)

Option 2 : Rs. 465

Given:

Principal is 15000

Rate is 10%

Time is 3 years

Formula used:

S.I. = (P × r × t)/100

C.I. = P{1 + (r/100)}t - P

Here P = Principle

r = Rate%

t = Time

Calculation:

S.I. = (15000 × 10 × 3)/100

⇒ S.I. = 150 × 10 × 3

⇒ S.I. = 4500

And, C.I. = 15000{1 + (10/100)}3 - 15000

⇒ C.I. = 15000{1 + (1/10)}3 - 15000

⇒ C.I. = 15000(11/10)3 - 15000

⇒ C.I. = 15 × 1331 - 15000

⇒ C.I. = 19965 - 15000

⇒ C.I. = 4965

Now, difference between C.I. and S.I. = 4965 - 4500

∴ The difference between C.I. and S.I. is 465

Alternate Method

Difference between C.I. and S.I. for 3 years = P × r2(300 + r)/1003

⇒ Difference between C.I. and S.I. = 15000 × 102(300 + 10)/1003

⇒ Difference between C.I. and S.I. = 15000 × 100(300 + 10)/1000000

⇒ Difference between C.I. and S.I. = 15 × 31

∴ Difference between C.I. and S.I. is 465.

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