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51. The population of a town was reduced by 12% in the year 2010, In 2011, it was again reduced by 12%. What is the percentage in the population in the beginning of 2012?
  A.  22.56%
  B.  18.16%
  C.  24.36%
  D.  21.75%
     
   
View Answer

Shortcut:
If a population decreases first by a% and again the decreases by b%, then there is
(
−a − b +
ab / 100
)
% net decrease.
Here, a = 12, b = 12
Using these values in the shortcut, we get:
Net change =
(
− 12 − 12 +
12x12 / 100
)
% =
(
− 24 +
144 / 100
)
% = −24 + 1.44 = −22.56%
Hence, net decrease of 22.56% in the population.

52. The difference between a discount of 35% and two successive discounts of 20% and 20% on a certain bill was Rs 22. Find the amount of the bill.
  A.  Rs 2,800
  B.  Rs 2,200
  C.  Rs 3,200
  D.  Rs 1,400
     
   
View Answer

Equivalent discount of two successive discounts =
(
20 + 20 −
20x20 / 100
)
%
=
(
40 −
400 / 100
)
% = 40 − 4 = 36%
Now as per question, difference between 35% discount and 36% discount = Rs 22 ⇒ 36% − 35% = 22
∴ Amount of the bill = 22 x 100 = 2200

53. The tax on commodity is diminished by 20% and its consumption increases by 15%. Find the effect on revenue.
  A.  10%
  B.  4%
  C.  -8%
  D.  -2%
     
   
View Answer

Shortcut:
If a tax on commodity decreases first by a% and its compumption increases by b%, then there is
(
−a + b −
ab / 100
)
% decrease or increase on revenue, +ve or -ve sign will show gain and loss respectively.
Here, a = 20, b = 15
Using these values in the shortcut, we get:
Net change =
(
−20 + 15 −
20x15 / 100
)
% =
(
−5 −
300 / 100
)
% = −5 − 3 = −8%
Hence, net decrease of 8% in the revenue.

54. If the price is increased by 10% and the sale is decreased by 5%, then what will be the effect on income?
  A.  +1.5%
  B.  +6%
  C.  +4.5%
  D.  +6.5%
     
   
View Answer

Shortcut:
If the price on commodity increases first by a% and its sale decreases by b%, then there is
(
a − b −
ab / 100
)
% decrease or increase on revenue, +ve or -ve sign will show gain and loss respectively.
Here, a = 10, b = 5
Using these values in the shortcut, we get:
Net change =
(
10 − 5 −
10x5 / 100
)
% =
(
5 −
50 / 100
)
% = 5 − 0.5 = +4.5%
Hence, net increase of 4.5% in the revenue or income.

55. If the price is decreased by 12% and sale is increased by 10% then what will be the effect on income?
  A.  -3.2%
  B.  +5%
  C.  +2 %
  D.  -2%
     
   
View Answer

Shortcut:
If the price on commodity decreases first by a% and its sale increases by b%, then there is
(
−a + b −
ab / 100
)
% decrease or increase on revenue, +ve or -ve sign will show gain and loss respectively.
Here, a = 12, b = 10
Using these values in the shortcut, we get:
Net change =
(
−12 + 10 −
12x10 / 100
)
% =
(
−2 −
120 / 100
)
% = −2 −
6 / 5
% = −2 − 1.2 = −3.2%
Hence, net decrease of 3.2% in the revenue or income.

56. Tax on commodity is diminished by 25% and consumption increases by 25%. Find the effect on revenue.
  A.  -2%
  B.  +5.25%
  C.  -3%
  D.  -6.25%
     
   
View Answer

Shortcut:
If the price on commodity decreases first by a% and its consumption increases by b%, then there is
(
−a + b −
ab / 100
)
% decrease or increase on revenue, +ve or -ve sign will show gain and loss respectively.
Here, a = 25, b = 25
Using these values in the shortcut, we get:
Net change =
(
−25 + 25 −
25x25 / 100
)
% =
(
0 −
625 / 100
)
% = −6.25%
Hence, net decrease of 6.25% in the revenue or income.

57. The land holding of a person is decreased by 10% due to late monsoon, the production decreases by 8%. Then what is the effect on the revenue?
  A.  -17.2%
  B.  -14.2%
  C.  +15.2%
  D.  -19.2%
     
   
View Answer

Shortcut:
If the land holding of a person decreases by a% and his production decreases by b%, then there is
(
−a − b +
ab / 100
)
% decrease or increase on revenue, +ve or -ve sign will show gain and loss respectively.
Here, a = 10, b = 8
Using these values in the shortcut, we get:
Net change =
(
−10 − 8 +
10x8 / 100
)
% =
(
−18 +
80 / 100
)
% = −18 + 0.8 = −17.2%
Hence, net decrease of 17.2% in the revenue or income.

58. The number of seats in a cinema hall is decreased by 5%. The price on a ticket is also decreased by 5%. What is the effect on the revenue collected?
  A.  -9.75%
  B.  -8.75%
  C.  -11.75%
  D.  +7.75%
     
   
View Answer

Shortcut:
If the number of seats decreases by a% and the price of tickets gets also decreases by b%, then there is
(
−a − b +
ab / 100
)
% decrease or increase on revenue, +ve or -ve sign will show gain and loss respectively.
Here, a = 5, b = 5
Using these values in the shortcut, we get:
Net change =
(
−5 − 5 +
5x5 / 100
)
% =
(
−10 +
25 / 100
)
% = −10 + 0.25 = −9.75%
Hence, net decrease of 9.75% in the revenue or income.

59. The number of seats in a cinema hall is increased by 25%. The price on a ticket is also increased by 10%. What is the effect on the revenue collected?
  A.  +33.5%
  B.  +37.5%
  C.  -24.5%
  D.  +30.5%
     
   
View Answer

Shortcut:
If the number of seats increases by a% and the price of tickets gets also increases by b%, then there is
(
a + b +
ab / 100
)
% net increase.
Here, a = 25, b = 10
Using these values in the shortcut, we get:
Net change =
(
25 + 10 +
25x10 / 100
)
% =
(
35 +
250 / 100
)
% =
(
35 +
5 / 2
)
% = 35 + 2.5 = 37.5%
Hence, net increase of 37.5% in the revenue.

60. The landholding of a person is increased by 10%. Due to early monsson, the production increases by 10%. Then what is the effect on renenue?
  A.  -24%
  B.  +11%
  C.  +27%
  D.  +21%
     
   
View Answer

Shortcut:
If the landholding increases by a% and the production also increases by b%, then there is
(
a + b +
ab / 100
)
% net increase.
Here, a = 10, b = 10
Using these values in the shortcut, we get:
Net change =
(
10 + 10 +
10x10 / 100
)
% =
(
20 +
100 / 100
)
% = 20 + 1 = 21%
Hence, net increase of 21% in the revenue.

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