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51. Ajay lends Rs 300 for 5 years and Rs 375 for 2 years, received altogether Rs 225 as a simple interest. Find the rate per annum.
  A.  10%
  B.  8%
  C.  13%
  D.  11%
     
   
View Answer

Shortcut:
If a person lends Rs Z1 for t1 years and Rs Z2 for t2 years received altogether Rs I as a simple interet, the rate per cent per annum is
100 x I / Z1 x t1 + Z2 x t2
]%.
Here, Z1 = 300, t1 = 5, Z2 = 375, t2 = 2, I = 225
Using these values in shortcut, we get:
Required rate =
100 x 225 / 300 x 5 + 375 x 2
% =
100 x 225 / 1500 + 750
%
=
100 x 225 / 2250
% = 10
Hence, the rate is 10%.

52. On Rs 1250 invested at a S.I rate 4 per cent per annum, Rs 250 is obtained as interest in certain years. In order to earn Rs 1000 as interest on Rs 2000, in the same number of years, what should be the rate of S.I?
  A.  7%
  B.  12%
  C.  10%
  D.  9%
     
   
View Answer

Shortcut:
On Rs Z1 invested at a simple interest rate r1 per cent per annum, Rs I1 is obtained as interest in certain years. In order to earn Rs I2 as interest on Rs Z2 in the same number of years, the rate of simple interest is given by
I2 / I1
x
Z1 / Z2
x r1%
Here, Z1 = 1250, r1 = 4, I1 = 250, I2 = 1000, Z2 = 2000
Using these values in shortcut, we get:
Required rate =
1000 / 250
x
1250 / 2000
x 4% =
1000 / 250
x
1250 / 2000
x 4%
= 4 x 0.625 x 4 = 10
Hence, the rate is 10%.

53. In what time will a sum of money double itself at 10% per annum S.I being charged?
  A.  11 years
  B.  10 years
  C.  14 years
  D.  20 years
     
   
View Answer

Shortcut:
The time in which a sum of money becomes n times itself at r% per annum simple interest is given by
n − 1 / r
x 100
Here, n = 2, r = 10
Using these values in shortcut, we get:
Required time =
2 − 1 / 10
x 100 = 10
Hence, the time is 10 years.

54. At what rate per cent S.I will a sum of money double itself in 20 years.?
  A.  5%
  B.  3%
  C.  4%
  D.  7%
     
   
View Answer

Shortcut:
The rate in which a sum of money becomes n times itself in t time is given by
n − 1 / t
x 100
Here, n = 2, t = 20
Using these values in shortcut, we get:
Required rate =
2 − 1 / 20
x 100 = 5
Hence, the rate is 5%.

55. The S.I on a sum of money will be Rs 600 in 10 years. If the principal is trebled after 5 years, the total interest at the end of 10 years will be:
  A.  Rs 950
  B.  Rs 1200
  C.  Rs 1000
  D.  Rs 1350
     
   
View Answer

Let the sum is Rs z.
SI = Rs 600, t = 10 years
∴ Rate =
600 x 100 / z x 10
% =
6000 / z
%
Simple Interest for first 5 years = Rs
z x 5 x 6000 / 100 x z
% = Rs 300
Simple Interest for last 5 years = Rs
3z x 5 x 6000 / 100 x z
% = Rs 900
Hence, total interest at the end of 10 years = Rs 1200

56. If X is the simple interest on Y and Y is the simple interest on Z, the rate % and the time being the same in both cases, what is the relation between X,Y and Z?
  A.  Y2=XZ
  B.  X2=YZ
  C.  Y3=XZ
  D.  Z2=XY
     
   
View Answer

X =
Y x r x t / 100
and Y =
Z x r x t / 100

or
X / Y
=
Y / Z

or Y2 = XZ

57. Out of a certain sum,
1 / 3
rd is invested at 3%, 1/6th at 6% and the rest at 8%. If the S.I for 2 years form all these investments amounts to Rs 600, find the original sum.
  A.  Rs 4600
  B.  Rs 5500
  C.  Rs 3800
  D.  Rs 5000
     
   
View Answer

Shortcut:
A person invested 1/n1 of his capital at r1%, 1/n2 at r2% and the remainder 1/n3 at r3%. If his annual income is Rs Z, the capitalis given by Rs
Z x 100 / (r1/n1 + r2/n2 + r3/n3)
.
Here, Z = 600, r1 = 3, r2 = 6, r3 = 8, n1 = 3, n2 = 6, n3 = (1 − 1/3 − 1/6) or 1/2 , K = 600/2 = 300
Using these values in shortcut, we get:
Required sum = Rs
300 x 100 / [3/3 + 6/6 + 8/2]
= Rs
300 x 100 / [1 + 1 + 4]

= Rs
300 x 100 / 6
= 5000
Hence, the sum is Rs 5000.

58. A certain sum of money at simple interest amounts to Rs 1012 in 2
1 / 2
years and to Rs 1067.20 in 4 years. The rate of interest per annum is:
  A.  3%
  B.  2%
  C.  4%
  D.  5%
     
   
View Answer

Shortcut:
If a sum amounts to Rs Z1 in t1 year and Rs Z2 in t2 years at simple rate of interest, then rate per annum is given by
100(Z2 − Z1) / Z1 x t2 − Z2 x t1
%.
Here, Z1 = 1012, Z2 = 1067.20, t1 = 5/2 or 2.5, t2 = 4
Using these values in shortcut, we get:
Required rate =
100(1067.2 − 1012) / 1012 x 4 − 1067.20 x 2.5
% =
100 x 55.2 / 4048 − 2668
%
=
5520 / 1380
% =
552 / 138
% = 4%
Hence, the rate is 4%.

59. A certain sum of money at S.I amounts to Rs 1260 in 2 years and to Rs 1350 in 5 years. The rate per cent per annum is:
  A.  5%
  B.  2.5%
  C.  4%
  D.  1.5%
     
   
View Answer

Shortcut:
If a sum amounts to Rs Z1 in t1 year and Rs Z2 in t2 years at simple rate of interest, then rate per annum is given by
100(Z2 − Z1) / Z1 x t2 − Z2 x t1
%.
Here, Z1 = 1260, Z2 = 1350, t1 = 2, t2 = 5
Using these values in shortcut, we get:
Required rate =
100(1350 − 1260) / 1260 x 5 − 1350 x 2
% =
100 x 90 / 6300 − 2700
%
=
100 x 90 / 3600
% =
100 / 40
% =
5 / 2
% = 2.5%
Hence, the rate is 2.5%.

60. At what rate of interest per annum will a sum doubles itself in 8 years?
  A.  12
1 / 2
%
  B.  9
2 / 5
%
  C.  13
3 / 7
%
  D.  11
9 / 2
%
     
   
View Answer

Shortcut:
The rate in which a sum of money becomes n times itself in t time is given by
n − 1 / t
x 100
Here, n = 2, t = 8
Using these values in shortcut, we get:
Required rate =
2 − 1 / 8
x 100 =
25 / 2
% = 12
1 / 2
%
Hence, the rate is 5%.

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