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11. If the simple interest on Rs 4000 increases by Rs 40, when the time increases by 4 years. Find the rate percent per annum.
  A.  0.25%
  B.  1%
  C.  0.50%
  D.  1.25%
     
   
View Answer

Shortcut:
To find the rate
r =
100 x S.I / Pt

P = principal
r = rate
t = time
Here, P = 4000, S.I = 40, t = 4
Using these values in shortcut, we get:
r =
100 x 40 / 4000 x 4
= 0.25
Hence, the rate is 0.25%.

12. A boy deposits Rs 3000 in a bank at 4% per annum and Rs 2000 in SBI at 14% per annum. Find the rate of interest for the whole sum.
  A.  6%
  B.  3%
  C.  8%
  D.  5%
     
   
View Answer

Shortcut:
If a person deposits Rs Z1 in a bank at r1% per annum and Rs Z2 in another bank at r2% per annum then the rate of interest for the whole sum is
r =
Z1 x r1 + Z2 x r2 / Z1+ Z2

Here, Z1 = 3000, r1 = 4, Z2 = 2000, r2 = 14
Using these values in shortcut, we get:
r =
3000x 4 + 2000 x 14 / 3000 + 2000
=
12000 + 28000 / 5000
=
40000 / 5000
= 8
Hence, the rate is 8%.

13. The simple interest on a sum of money is
1 / 9
of the principal and the number of years is equal to the rate per cent per annum. Find the rate per cent.
  A.  5
3 / 7
%
  B.  2
1 / 2
%
  C.  3
1 / 3
%
  D.  3
4 / 7
%
     
   
View Answer

Shortcut:
If the simple interest on a sum of money is 1/n of the principal, and the number of years is equal to the rate per cent per annum, then the rate per cent is r =
[√
(
100 x
1 / n
)
]

Here, n = 9
Using these values in shortcut, we get:
r =
[√
(
100 x
1 / 9
)
]
=
10 / 3
= 3
1 / 3
%
Hence, the rate is 3
1 / 3
%.

14. If the simple interest on Rs 1400 be more than the interest on Rs 1,000 by Rs 30 in 3 years, find the rate percent per annum.
  A.  2.5%
  B.  4.5%
  C.  1.5%
  D.  3.25%
     
   
View Answer

Shortcut:
When Princiapl (P) changes form P1 to P2, then SI1 - SI2 =
(P1 − P2) x r x t / 100

Here, P1 = 1400, P2 = 1000, SI1 − SI2 = 30, t = 3
Using these values in shortcut, we get:
30 =
(1400 − 1000) x r x 3 / 100

30 =
400 x r x 3 / 100

30 = 4 x r x 3
r =
5 / 2
= 2.5%
Hence, the rate is 2.5%.

15. If simple interest on Rs 4000 increases by Rs 80, when the rate % increases by 2% per annum. Find the time.
  A.  1 year
  B.  1.5 year
  C.  2 year
  D.  0.5 year
     
   
View Answer

Shortcut:
When Rate (r) changes form r1 to r2, then SI1 − SI2 =
P x (r1 − r2) x t / 100

Here, P = 4000, SI = 80, (r1 − r2) = 2
Using these values in shortcut, we get:
80 =
4000 x 2 x t / 100

80 = 40 x 2 x t
t = 1
Hence, the time is 1 year.

16. What annual payment will discharge a debt of Rs 770 due in 5 years, the rate of interest being 5% per annum?
  A.  Rs 159
  B.  Rs 154
  C.  Rs 160
  D.  Rs 140
     
   
View Answer

Shortcut:
The annual payment that will discharge a debt of Rs Z due in t years at the rate of interest r% per annum is =
100 x Z / 100 x t + [rt(t − 1)]/2

Here, Z = 770, t = 5, r = 5
Using these values in shortcut, we get:
Annual Payment =
100 x 770 / 100 x 5 + [5 x 5(5 − 1)]/2

=
100 x 770 / 500 + [5 x 5 x 4]/2

=
100 x 770 / 500 + 5 x 5 x 2

=
100 x 770 / 500 + 50

=
100 x 770 / 550

=
100 x 7 / 5
= 140
Hence, the annual payment is Rs 140.

17. Prem invested an amount of Rs 12000 at the simple interest rate of 10 per cent per annum and another amount at the simple interest rate of 20 per cent per annum. The total interest earned at the end of one year on the total amount invested became 14 per cent per annum. Find the total amount invested.
  A.  Rs 20,000
  B.  Rs 17,000
  C.  Rs 21,500
  D.  Rs 19,500
     
   
View Answer

Shortcut:
If a person deposit Rs Z1 in a bank at r1% per annum and Rs Z2 in another bank at r2% per annum then the rate of interest for the whole sum is r =
Z1 x r1 + Z2 x r2 / Z1+ Z2

Here, Z1 = 12000, r1 = 10, Z2 = ?, r2 = 20
Using these values in shortcut, we get:
14 =
12000 x 10 + Z2 x 20 / 12000 + Z2

14 ( 12000 + Z2) = 120000 + 20Z2
168000 + 14Z2 = 120000 + 20Z2
168000 − 120000 = 20Z2 − 14Z2
48000 = 6Z2
Z2 =
48000 / 6
= 8000
∴ Another amount is Rs 8000.
Total amount = Z1 + Z2 = 12000 + 8000 = Rs 20000
Hence, total amount invested was Rs 20,000.

18. The rate of interest for the first 2 years is 3% per annum, for the next 3 years is 8% per annum and for the period beyond 5 years 10% per annum. If a man get Rs 1600 as a simple interest for 6 years, how much money did he deposit?
  A.  Rs 4000
  B.  Rs 2700
  C.  Rs 4300
  D.  Rs 3600
     
   
View Answer

Shortcut:
The rate of interest for the first t1 years is r1 per annum, for the next t2 years is r2% per annumand for the period beyound t3 years r3% per annum. If a man gets Rs Z as a simple interest for t years, he deposited Principal =
S.I x 100 / t1r1 + t2r2 + t3r3 + .....+ tnrn

Here, SI = 1520, t1 = 2, r1 = 3, t2 = 3, r2 = 8, t3 = 1 (t − t1 − t2), r3 = 10
Using these values in shortcut, we get:
=
1520 x 100 / 2x3 + 3x8 + 1x10

=
1520 x 100 / 6 + 24 + 10

=
1600 x 100 / 40
= 40 x 100 = 4000
Hence, total amount invested was Rs 4,000.

19. Amit borrowed a sum of money from Jaya at the rate of 8% per annum simple interest for the first four years, 10% per annum for the next 6 years and 12% per annum for the period beyond 10 years. If he pays a total of Rs 12,160 as interest only at the end of 15 years, how much money did he borrow?
  A.  Rs 7,300
  B.  Rs 8,000
  C.  Rs 8,300
  D.  Rs 7,900
     
   
View Answer

Shortcut:
The rate of interest for the first t1 years is r1 per annum, for the next t2 years is r2% per annumand for the period beyound t3 years r3% per annum. If a man gets Rs Z as a simple interest for t years, he deposited Principal =
S.I x 100 / t1r1 + t2r2 + t3r3 + .....+ tnrn

Here, SI = 12160, t1 = 4, r1 = 8, t2 = 6, r2 = 10, t3 = 5 (t − t1 − t2), r3 = 2
Using these values in shortcut, we get:
=
12160 x 100 / 4x8 + 6x10 + 5x12

=
12160 x 100 / 32 + 60 + 60

=
12160 x 100 / 152
= 80 x 100 = 8000
Hence, total amount invested was Rs 8,000.

20. A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?
  A.  15%
  B.  23%
  C.  17%
  D.  20%
     
   
View Answer

Shortcut:
If a sum of money becomes 'n' times in 't' years at SI, the rate of interest is given by
100(n − 1) / t

Here, n = double i.e 2, t = 5
Using these values in shortcut, we get:
r =
100(2 − 1) / 5
= 20%
Hence, rate of interest is 20%.

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