Neeta borrowed some money at the rate of 6% per annum for the first 3 yr. at the rate of 9% per annum for the next 5 yr and a the rate of 13% per annum for the period beyond 8 yr. If she pays a total interest of ? 8160 at the and of 11 yr how much money did she borrow?

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

Given, A₁ = ? 1350, A₂ =? 1620
T₁ = 5 yr and T₂ = 8 yr
Let principal amount be ? P.
? In time = 8 - 5 = 3 yr
Simple interest will be
1620 - 1350 = ? 270
? R = [(A₂ - A₁ ) x 100] / [A₁ T₂ - A₂ T₁]
= [(1620 - 1350) x 100] / [(1350 x 8) - (1620 X 5)]
= (270 x 100)/[10800 - 8100]
= 27000/2700
? R = 10%
? P = (SI x 100) / (R x T)
= (270 x 100) / (10 x 3)
= ? 900

Give, time = 42 months.
= (42/12) yr = 3¹/₂ yr
= 7 half - yr,
rate = 13/2% half - yearly

SI = (20000 x 13 x 7)/(100 x 2) = ? 9100
? Amount (A) = 20000 + 9100
= ? 29100

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

In the case I,
SI = (P x R x T) /100 = (24200 x 4 x 6) / 100 = ? 5808

? Amount = Principal + SI
SI = 24200 + 5808 = 30008

In the case II,
SI = (30008 x 4 x 4) / 100 = ? 4801.28

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