Pratap borrowed some money from Arun at simple interest. The rate of interest for the first 3 years was 12% for the next 5 years was 16% and beyond this it was 20%. If the simple interest for 11 years was more than the money borrowed by Rs. 6080. What was the money borrowed?

Let the principal be Rs. P
? Amount = Rs. 10080
? Simple interest = Amount - Principal = 10080 - P

&because Simple interest = (Principal x Rate x Time) / 100
? 10080 - P = (P x 16 x 5) / 100
? 10080 - P = 4P/5
? 50400 - 5P = 4P
? 50400 = 5P + 4P
? 50400 = 9P
? P = 50400/9 = Rs. 5600

r₁ = 5%
r₂ = 8%
r₃ = 10%
r₄ = 12%

t₁ = 3 years
t₂ = 2 years
t₃ = 4 years
t₄ = 12 - (3 + 2 + 4) = 3 years


? Principal = ( Interest x 100) / ( r₁ t₁ + r₂ t₂ + r₃ t₃ + r₄ t₄)
= (8560 x 100) / (5 x 3 + 8 x 2 + 10 x 4 + 12 x 3)
= 856000/107
= Rs. 8000

r₁ = 5%,
r₂ = 8%,
r₃ = 10%,

t₁ = 2 years
t₂ = 3 years,
t₃ = 8 - (2 + 3) = 3 years
? Principal = (Interest x 100) / [(r₁ x t₁) + (r₂ x t₂) + (r₃ x t₃ )]

= (1280 x 100) / (5 x 2 + 8 x 3 + 10 x 3)
= 128000/(10 + 24 + 30)
= 128000/64
=Rs. 2000

? A = (B x R x T) / 100 ....(i)
And B = (C x R x T) / 100 ...(ii)

From Eq. (i) and (ii)
? A/B = B/C
? B² = AC

Let sum= Rs. P
Then, [(P x 4 x 2) /100] + [(P x 6 x 4) / 100] + [(P x 8 x 3) /100] = 1120
? 56 x P = 112000
? P = 112000/56 = Rs. 2000

Let the first part be ? A.
second part be ? B
and third part be Rs C
According to the question.
(A x 2 x 3)/100 = (B x 3 x 4)/100 = (C x 4 x 5)/ 100
? 3A = 6B = 10C = k
? A = k/3, B = k/100 and C = k /10
Now, A + B + C = 1440
? k/3 + k/6 + k/10 = 1440 ? k = 2400
? so the difference = k/3 - k/10 = 7k/30 = 7/30 x 2400 = ? 560

Rest part = 1 - (1/3 + 1/6) = 1/2
Average rate per cent annum on the total sum
= [(1/3) x 3] + [(1/6) x 6] + [(1/2) x 8] = 6%
? P = (100 x SI)/(R x T) = (100 x 600)/(6 x 2) = ? 5000

Cost of the music system = ? 8000
Money paid at once = ? 3500
Money left = (8000 - 3500) = ? 4500
Time = (18/12) = 3/2 yr and R = 8% per annum
SI = PTR/100 = (4500 x 3/2 x 8)/100 = ? 540
Money to be paid at the end = (4500 + 540) = ? 5040
? Cost of music system = (3500 + 5040) = ? 8540

Let the sum be P and Q, respectively.
Then, (P x 6 x 2)/100 + (Q x 7 x 2)/100 = 792
? 6P + 7Q = 39600 ...(i)

Also P/2 = Q/3 ? 3P = 2Q ... (ii)

On solving Eqs . (i) and (ii), we get P = 2400 and Q = 3600
? Total sum = (2400 + 3600) = ? 6000

Let the money added be ? P, Then,
[(4800 + P) x 12 x 3]/100 - (4800 x 9 x 3)/100 = 720
? (4800 + P) x 36 - (4800 x 27) = 720 x 100
? (4800 + P) x 4 - (4800 x 3) = 8000
? 4800 + P - (1200 x 3 ) = 2000
? P + 1200 = 2000
? P = 800
So, money added is ? 800.