Mr. Pawan invests an amount of ? 242000 at the rate of 4% per annum for 6 yr to obtain a simple interest, later he invests the principal amount as well as the amount obtained as simple interest for another 4 yr at the same rate of interest. What amount of simple interest will be obtained at the end of the last 4 yr?

Let the money lent to Akshay = ? P
Then, money lent to Brijesh = ? (10000 - P) [as total amount = ? 10000]
SI for Akshay = (P x 15 x 2)/100 = 3P/10
SI for Brijesh = {(10000 - P) x 18 x 2}/100 = 9/25 (10000 - P)

According to the given condition, (3P/10) - [(9/25) x ( 10000 - P ) = 360
[as SI (Akshay) - SI (Brijesh) = 360]

? (3P/10) - 3600 + 9P/25 = 360
? 3P/10 + 9P/25 = 360 + 3600 = 3960
? 33P/50 = 3960
? P = 3960 x 50/33
? P = 6000

? The amount of money lent to Brijesh
= 10000 - 6000 ? 4000

Let the sum borrowed = P
Then, according to the question,
[(P x 6 x 3)/100] + [(P x 9 x 5)/100] + [(P x 13 x 3)/100] = 8160
? (18P + 45P +39P) / 100 = 8160
? 102P/100 = 8160
? P = (8160 x 100)/102
? P = ? 8000

Let the sum lent at 5% = P
? Sum lent at 8% = (1550 - P)
Then, [(P x 5 x 4)/100] + [{(1550 - P) x 8 x 4}/100] = 400
? 20P - 32P + 1550 x 32 = 40000
? - 12P + 49600 = 40000
? - 12P = - 9600
? p = ? 800
Sum lent at 8% = 1550 - 800 = ? 750
? Required ratio = 800 : 750 = 16 : 15

By formula, P = (A₂T₁ - A₁T₂) / (T₁ - T₂)
Here, A₁ = ? 944, T₁ = 3
A₂ = ? 1040, T₂ = 5
? P = [(1040 x 3) - (944 x 5)] / (3 - 5)
= (3120 - 4720) / (-2)
= (-1600) / (-2)
= ? 800
? Principal = ? 800

Amount = ? 8000
Time (T) = 4 yr; Principal (P) = ? 6000
Simple interest (SI) = (A - P)
= Amount - Principal
= 8000 - 6000 = ? 2000

Rate (R) = ?
According to the formula. SI = (P x R x T)/100
? 2000 = (6000 x R x 4)
? R = (6000 x 100)/(6000 x 4) = (25/3) %

Now, again Amount (A) = ? 700
Principle (P) = ? 525, Time (T) = ?
Rate (R) = 25/3%
Simple interest = A - P
? 700 - 525 = ? 175

Using formula, SI = (P x R x T) / 100
? 175 = [525 x (25/3) x T] / 100
? T = (175 x 100 x 3) / (525 x 25)
= 4 yr

Let the rate of interest allowed by bank be r%
According to the question,
[(12000 x 5 x 10)/100] - [(12000 x 3 x r)/100] = 3320
? 6000 - 360r = 3320
? 360r = 6000 - 3320 = 2680
? r = 2680/360 = 7⁴/₉%

Let a, b and c be the amount invested in schemes P, Q and R, respectively.

Then, according to the question,
[(a x 10 x 1)/100] + [(b x 12 x 1)/100] + [(c x 15 x 1)/100] = 3200

? 10a + 12b + 15x = 320000 .....(i)
Now, c = 240% of b = 12b/5 ....(ii)
and c = 150% of a = 3a/2
? a = 2c/3 = (2/3 x 12/5) b = 8b/5 .....(iii)

From Eqs. (i), (ii) and (iii), we get
16b + 12b + 36b = 320000
? 64b = 320000
? b = 5000
? Sum invested in scheme Q = ? 5000

Here, A = ? 8800, T =2 yr, R = 5%
We know
SI = ART/(100 + RT) = (8800 x 5 x 2) / (100 + 5 x 2)
= (8800 x 10) / 110
= ? 800

Let the sum be Rs . 100 then
S.I. = Rs.(100 x 5 x 2/100)= Rs. 10
C.I = Rs. [{100 x (1 + 5/100)²} - 100] = Rs. 41/4

? Difference between C.I and S.I = Rs. (41/4 - 10) = Re. 0.25
? 0.25 : 150 : : 100 : P
? P = (1.50 x 100) / 0.25 = Rs. 600

Let the principle is P
so compound interest = p x ( 1 + (12.5/100))sup>2 - p = 170
? p x (112.5/100) x (112.5/100) - p = 170
? P [ 12656.25 - 10000 ] = 170 x 10000
? p = (170 x 10000) / 2656.25

Simple interest SI = (P x T x R )/100
= [{(170 x 10000) / 2656.25} x 2 x 12.5] / 100
= 160