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21. If the CI on a certain sum for 2 years at 3% be Rs 609, what would be the S.I?
  A.  Rs 600
  B.  Rs 580
  C.  Rs 610
  D.  Rs 650
     
   
View Answer

Shortcut:
If the compound interest (C.I) on a certain sum for t years at r% be Rs Z, then the simple interest (S.I) is given by
rt / 100[(1 + r/100)t) − 1]
x Z
Here, Z = 609, t = 2, r = 3
Using these values in shortcut, we get:
S.I =
3 x 2 / 100[(1 + 3/100)2) − 1]
x 609
S.I =
3 / 50[{(100 + 3)/100}2) − 1]
x 609
S.I =
3 / 50[(103/100)2 − 1]
x 609
S.I =
3 / 50[(103 x 103)/(100 x 100) − 1]
x 609
S.I =
3 / 50[10609/10000 − 1]
x 609
S.I =
3 / 50[(10609 − 10000)/10000]
x 609
S.I =
3 / 50[609/10000]
x 609
S.I =
3 x 10000 / 50 x 609
x 609
S.I = 3 x 200 = 600
Hence, simple interest is Rs 600.

22. The simple interest on a certain sum of money for 2 years at 10% per annum is Rs 600. Find the compound interest at the same rate and for the same time.
  A.  Rs 655
  B.  Rs 630
  C.  Rs 600
  D.  Rs 595
     
   
View Answer

Shortcut:
If the simple Interest on a certain sum for 2 years at r% be Rs 'Z' then the compound interest is given by the
r + 200 / 200
x Z
Here, Z = 600, t = 2, r = 10
Using these values in shortcut, we get:
C.I =
10 + 200 / 200
x 600
S.I =
210 / 200
x 600
S.I = 210 x 3 = 630
Hence, compound interest is Rs 630.

23. The compound interest on a certain sum for 2 years is Rs 42 and simple interest is Rs 40. Find the rate of interest per annum and the sum:
  A.  Rate: 8%; Sum: Rs 180
  B.  Rate: 10%; Sum: Rs 200
  C.  Rate: 13%; Sum: Rs 240
  D.  Rate: 11%; Sum: Rs 220
     
   
View Answer

Shortcut:
If the compound interest on a certain sum for 2 years is Rs Z and the simple interest is Rs K, then the rate of interest per annum is given by
2(Z − K) / K
x 100 %
Here, Z = 42, t = 2, K = 40
Using these values in shortcut, we get:
rate =
2(42 − 40) / 40
x 100 %
=
2 x 2 / 40
x 100 %
=
1 / 10
x 100 % = 10%
Hence, rate of interest is 10%.
Sum =
K x 100 / r x t

=
40 x 100 / 10 x 2
= 200
Hence, the sum if Rs 200.

24. On a certain sum of moeny, the simple interest for 2 years is Rs 40 at the rate of 5% per annum. Find the difference in C.I and S.I.
  A.  Re 1
  B.  Re 5
  C.  Re 3
  D.  Re 2
     
   
View Answer

Shortcut:
If on a certain sum of money, the simple interest for 2 years at the rate of r% per annum is Rs Z, then the difference in compound interest and simple interest is Rs
Z x r / 200

Here, Z = 40, t = 2, r = 5
Using these values in shortcut, we get:
(C.I − S.I) = Rs
40 x 5 / 200
= Rs 1
Hence, the difference is of Rs 1.

25. The difference between the compound interest and the simple interest on a certain sum of money at 5% per annum for 2 years is Rs 1. Find the sum.
  A.  Rs 380
  B.  Rs 400
  C.  Rs 430
  D.  Rs 450
     
   
View Answer

Shortcut:
If the difference between the compound interest and S.I on a certain sum of money for 2 years at r% is Rs Z, then the sum is
Z x 100 x 100 / r x r

Here, Z = 1, t = 2, r = 5
Using these values in shortcut, we get:
Sum =
1 x 100 x 100 / 5 x 5
= 400
Hence, the sum is Rs 400.

26. Find the difference between the compound interest and the simple interest for the sum Rs 2500 at 4% per annum for 2 years.
  A.  Rs 4
  B.  Rs 2
  C.  Rs 6
  D.  Rs 5
     
   
View Answer

Shortcut:
On a certain sum of money say Rs Z, the difference between the C.I and S.I for 2 years at r% is given by
Z x r x r / 100 x 100

Here, Z = 2500, t = 2, r = 4
Using these values in shortcut, we get:
C.I − S.I =
2500 x 4 x 4 / 100 x 100
= 4
Hence, the difference is Rs 4.

27. If the difference between CI and SI on a certain sum of money for 3 years at 5% per annum is Rs 61, find the sum.
  A.  Rs 8500
  B.  Rs 8200
  C.  Rs 7800
  D.  Rs 8000
     
   
View Answer

Shortcut:
If the difference between the compound interest and S.I on a certain sum of money for 3 years at r% is Rs Z, then the sum is
Z x 100 x 100 x 100 / r x r x (300 + r)

Here, Z = 61, t = 3, r = 5
Using these values in shortcut, we get:
Sum =
61 x 100 x 100 x 100 / 5 x 5 x (300 + 5)

=
61 x 100 x 100 x 100 / 5 x 5 x 305
= 4 x 20 x 100
Hence, the difference is Rs 8000.

28. Find the difference between CI and SI on Rs 7000 for 3 years at 2.5% per annum.
  A.  Rs 13.254
  B.  Rs 11.234
  C.  Rs 13.234
  D.  Rs 14.364
     
   
View Answer

Shortcut:
On a certain sum of money Rs Z, the difference between C.I and SI for 3 years at r% per annum is given by
Z x r x r x (300 + r) / 100 x 100 x 100

Here, Z = 7000, t = 3, r = 2.5
Using these values in shortcut, we get:
C.I − S.I =
7000 x 2.5 x 2.5 x (300 + 2.5) / 100 x 100 x 100

=
7 x 2.5 x 2.5 x 302.5 / 10 x 100

=
7 x 25 x 25 x 3025 / 10 x 10 x 10 x 10 x 100

=
7 x 121 / 2 x 2 x 2 x 2 x 4

=
847 / 64
= 13.234
Hence, the difference is of Rs 13.234

29. An amount of money grows upto Rs 4000 in 2 years and upto Rs 5000 in 3 years on compound interest. Find the rate percent.
  A.  20%
  B.  25%
  C.  27%
  D.  23%
     
   
View Answer

Shortcut:
If an amount of money grows upto Rs Z1, in t years and upto Rs Z2 in (t + 1)years on compound interest, then the rate per cent is given by
(Z2 − Z1)100 / Z1

Here, Z1 = 4000, t = 3, Z2 = 5000
Using these values in shortcut, we get:
Rate =
(5000 − 4000)100 / 4000

=
1000 x 100 / 4000
= 25
Hence, the rate is 25%.

30. A certain amount of money at compound interest grows upto Rs 50000 in 15 years and up to Rs 52000 in 16 years. Find the rate per cent annum.
  A.  4%
  B.  5%
  C.  2%
  D.  1%
     
   
View Answer

Shortcut:
If an amount of money grows upto Rs Z1, in t years and upto Rs Z2 in (t + 1)years on compound interest, then the rate per cent is given by
(Z2 − Z1)100 / Z1

Here, Z1 = 50000, t = 16, Z2 = 52000
Using these values in shortcut, we get:
rate =
(52000 − 50000)100 / 50000

=
2000 x 100 / 50000
= 4
Hence, the rate is 4%.

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