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41. A sum of money doubles itself in 4 years at a simple interest. In how many years will it amount to 9 times itself?
  A.  28 years
  B.  32 years
  C.  35 years
  D.  26 years
     
   
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Shortcut:
If a sum of money becomes 'n' times in 't' years at a simple interest, then the time in which it will amount to 'z' times itself is given by
z − 1 / n − 1
t years.
Here, z = 9, n = 2 (double), t = 4
Using these values in shortcut, we get:
Required sum =
9 − 1 / 2 − 1
x 4 =
8 / 1
x 4 = 32
Hence, the time is 32 years.

42. The simple interest on Rs 1650 will be less than the interest on Rs 1770 at 5% simple interest by Rs 30. Find the time.
  A.  7 years
  B.  2 years
  C.  5 years
  D.  3 years
     
   
View Answer

Shortcut:
If the simple interest on Rs P1 is less than the interest on Rs P2 at r% simple interest by Rs Z, then the time is given by
Z x 100 / r(P2 − P1)
years.
Here, Z = 30, P1 = 1650, P2 = 1770, r = 5
Using these values in shortcut, we get:
Required time =
30 x 100 / 5 (1770 − 1650)
=
30 x 100 / 5 x 120
= 5
Hence, the time is 5 years.

43. Two equal amounts of money are deposited in two banks each at 15% per annum for 5 years and 4 years respectively. If the difference between their interests in Rs 144, find each sum.
  A.  Rs 895
  B.  Rs 930
  C.  Rs 840
  D.  Rs 960
     
   
View Answer

Shortcut:
Two equal amounts of money are deposited at r1% and r2% for t1 and t2 years respectively. If the difference between their interests is Idf then the sum is given by
Idf x 100 / r1t1 − r2t2
years.
Here, Idf = 144, r1 = 15, r2 = 15, t1 = 5, t2 = 4
Using these values in shortcut, we get:
Required sum =
144 x 100 / 15 x 5 − 15 x 4
=
144 x 100 / 75 − 60
=
144 x 100 / 15
= 960
Hence, the sum is Rs 960.

44. The difference between the interest received from two different banks on Rs 250 for 2 years is Rs 5. Find the difference between their rates.
  A.  1%
  B.  0.75%
  C.  0.5%
  D.  2%
     
   
View Answer

Shortcut:
If the difference between the interest received from two different banks on Rs Z for t years is Rs Idf, then the difference between their rates is given by
Idf x 100 / Z x t
per cent.
Here, Idf = 5, Z = 250, t = 2
Using these values in shortcut, we get:
Required rate =
5 x 100 / 250 x 2
% = 1%
Hence, the rate is 1%.

45. A sum of money at simple interest amounts to Rs 500 in 4 years and Rs 550 in 6 years. Find the rate of interest per annum.
  A.  5%
  B.  5.75%
  C.  6.25%
  D.  7.35%
     
   
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 = 500, Z2 = 550, t1 = 4, t2 = 6
Using these values in shortcut, we get:
Required rate =
100(550 − 500) / 500 x 6 − 550 x 4
% =
100 x 50 / 3000 − 2200
%
=
100 x 50 / 800
% =
25 / 4
% = 6.25%
Hence, the rate is 6.25%.

46. Raj borrows Rs 6000 from a bank at simple interest. After 3 years he paid Rs 2000 to the bank and at the end of 5 years from the date of borrowing he paid Rs 6600 to the bank to settle the account. Find the rate of interest.
  A.  8%
  B.  10%
  C.  13%
  D.  9%
     
   
View Answer

Shortcut:
If a person borrows Rs Z from a bank at simple interest and after t1 years he paid Rs z1 to the bank and at the end of t2 years from the date of borrowing he paid Rs z2 to the bank to settle the account, then the rate of interest is given by
z1 + z2 − Z) / z1 x t1 + t2(Z − z1)
x 100 %.
Here, Z = 6000, t1 = 3, z1 = 2000, t2 = 5, z2 = 6600
Using these values in shortcut, we get:
Required rate =
2000 + 6600 − 6000 / 2000 x 3 + 5(6000 − 2000)
x 100 %
=
8600 − 6000 / 6000 + (5 x 4000)
x 100 %
=
2600 / 6000 + 20000
x 100 %
=
2600 / 26000
x 100 % =
100 / 10
% = 10%
Hence, the rate is 10%.

47. Some amount out of Rs 6000 was lent at 6% per annum and the remaining at 4% per annum. If the total simple interest from both the fractions in 5 years was Rs 1500, find the sum lent at 6% per annum.
  A.  Rs 2940
  B.  Rs 3130
  C.  Rs 2600
  D.  Rs 3000
     
   
View Answer

Shortcut:
Some amount out of Rs Z was lent at r1% per annum and the remaining at r2% per annum. If the total simple interest from both the fractions in t years was Rs 'K' then the sum lent at r1% per annum was given by Rs
100K − Z x r2 x t / (r1 − r2)t
.
Here, Z = 6000, r1 = 6, r2 = 4, t = 5, K = 1500
Using these values in shortcut, we get:
Required sum =
100 x 1500 − 6000 x 4 x 5 / (6 − 4) x 5

=
150000 − 120000 / 2 x 5

=
30000 / 10
= 3000
Hence, the sum is Rs 3000.

48. Amit invested
1 / 3
of his capital at 7%,
1 / 4
at 8% and the remaining at 10%. If his annual income is Rs 255, find the capital.
  A.  Rs 3420
  B.  Rs 2700
  C.  Rs 3000
  D.  Rs 3200
     
   
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 = 255, r1 = 7, r2 = 8, r3 = 10, n1 = 3, n2 = 4, n3 = (1 − 1/3 − 1/4) or 5/12 , K = 1500
Using these values in shortcut, we get:
Required sum = Rs
255 x 100 / [7/3 + 8/4 + 10/(12/5)]
= Rs
255 x 100 / [7/3 + 2 + 25/6]

= Rs
255 x 100 / 51/6
= Rs
255 x 100 x 6 / 51
= 5 x 100 x 6 = 3000
Hence, the sum is Rs 3000.

49. The simple interest on certain sum of Rs 1600 is Rs 400, and the number of years is equal to the rate per cent per annum. Find the rate percent.
  A.  5%
  B.  2.5%
  C.  6%
  D.  4%
     
   
View Answer

Shortcut:
If the simple interet on certain sum 'Z' is 'I' and the number of years is equal to the rate per cent per annum, then the rate per cent or time is given by
[
√(
I x 100 / Z
)
]
%.
Here, I = 400, Z = 1600
Using these values in shortcut, we get:
Required rate =
[
√(
400 x 100 / 1600
)
]
%. =
[
√(
100 / 4
)
]
%. =
10 / 2
= 5
Hence, the rate is 5%.

50. A certain sum of money is borrowed by a person at 4% SI for 5 years. If he has to pay Rs 1600 as interest, find the total amount he has to pay.
  A.  Rs 9820
  B.  Rs 9600
  C.  Rs 9660
  D.  Rs 9500
     
   
View Answer

Shortcut:
If a borrower has to pay at r% simple interest per annum for t years and simple interest is given as Rs I, then the amount is given by I x
[
1 +
100 / r x t
]
.
Here, r = 4, t = 5, I = 1600
Using these values in shortcut, we get:
Required Amount = 1600 x
[
1 +
100 / 4 x 5
]
= 1600
[
1 +
100 / 20
]

= 1600 x [1 + 5] = 9600
Hence, the amount is Rs 9600.

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