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41. If A's salary is 25% more than that of B, then how much per cent is B's salary less than that of A?
  A.  22%
  B.  25%
  C.  18%
  D.  20%
     
   
View Answer

Shortcut:
If the first value is a% more than the second value, then the second is
[
a / 100 + a
x 100
]
% less than the first value.
Here, a = 25%
Using these values in the shortcut, we get:
Net change =
25 / 100 + 25
x 100% =
25 / 125
x 100% =
1 / 5
x 100% = 20%
Hence, B's salary is 20% less than that of A.

42. If A's salary is 30% less than that of B, then how much per cent is B's salary more than that of A?
  A.  41
6 / 7
%
  B.  43
6 / 7
%
  C.  42
6 / 7
%
  D.  40
6 / 7
%
     
   
View Answer

Shortcut:
If the first value is a% less than the second value, then the second is
[
a / 100 − a
x 100
]
% less than the first value.
Here, a = 30%
Using these values in the shortcut, we get:
Net change =
30 / 100 − 30
x 100% =
30 / 70
x 100% =
3 / 7
x 100% =
300 / 7
% = 42
6 / 7
%
Hence, B's salary is 42
6 / 7
% more than that of A.

43. The salary of a worker is first increased by 10% and then it was reduced by 10%. What was the change in his salary?
  A.  1% increase
  B.  1% decrease
  C.  5% increase
  D.  No change
     
   
View Answer

Shortcut:
If the value of a number is first increased by a% and later decreased by a%, then net change is always a derease which is equal to a% of a or
a2 / 100
.
Here, a = 10%
Using these values in the shortcut, we get:
Net change =
(10)2 / 100
=
100 / 100
= 1%
Hence, there will be 1% decrease in his salary.

44. The salary of a worker was first increased by 10% and then, decreased by 5%. What was the change in his salary?
  A.  +4.5% increase
  B.  +5.5% increase
  C.  +3.5% increase
  D.  -4.5% decrease
     
   
View Answer

Shortcut:
If the value of a number is first increased by a% and later decreased by b%, then there is
(
a − b −
ab / 100
)
% increase or decrease, as per positive or negative sign respectively.
Here, a = 10 b = 5
Using these values in the shortcut, we get:
Net change =
(
10 − 5 −
10x5 / 100
)
% = 5 −
50 / 100
% =
(
5 −
1 / 2
)
% = 5 − 0.5 = + 4.5
Hence, + sign shows net increase of 4.5% in his salary.

45. A shopkeeper marks the prices of his goods at 20% higher than the original price. After that, he allows a discount of 10%. What profit or loss did he get?
  A.  +9%
  B.  -8%
  C.  +7%
  D.  +8%
     
   
View Answer

Shortcut:
If the value of a number is first increased by a% and later decreased by b%, then there is
(
a − b −
ab / 100
)
% increase or decrease, as per positive or negative sign respectively.
Here, a = 20 b = 10
Using these values in the shortcut, we get:
Net change =
(
20 − 10 −
20x10 / 100
)
% =
(
10 −
200 / 100
)
% = 10 − 2 = +8
Hence, + sign shows net increase of 8% in his profit.

46. If the salary of a worker is first decreased by 20% and then increased by 10%. What is the percentage effect on his salary?
  A.  -10%
  B.  -12%
  C.  -15%
  D.  +12%
     
   
View Answer

Shortcut:
If the value of a number is first decreased by a% and later increased by b%, then there is
(
−a + b −
ab / 100
)
% increase or decrease, as per positive or negative sign repectively.
Here, a = 20, b = 10
Using these values in the shortcut, we get:
Net change =
(
−20 + 10 −
20x10 / 100
)
% =
(
−10 −
200 / 100
)
% = −10 − 2 = −12
Hence, − sign shows net decrease of 12% in his salary.

47. The population of a town was reduced by 12% in the year 2010. In 2011, it was increased by 15%. What is the percentage effect on the population in the begining of 2012
  A.  +3%
  B.  +1.5%
  C.  +1.2%
  D.  +2%
     
   
View Answer

Shortcut:
If the population is first decreased by a% and later increased by b%, then there is
(
− a + b −
ab / 100
)
% increase or decrease, as per positive or negative sign respectively.
Here, a = 12, b = 15
Using these values in the shortcut, we get:
Net change =
(
−12 + 15 −
12x15 / 100
)
% =
(
3 −
180 / 100
)
% =
(
3 −
9 / 5
)
% = 3 − 1.8 = +1.2
Hence, + sign shows net increase of 1.2% in the population.

48. A shopkeeper marks the prices of his goods at 20% higher than the original price. Due to increase in demand he again increases by 20%. What profit did he get?
  A.  44%
  B.  45%
  C.  40%
  D.  46%
     
   
View Answer

Shortcut:
If a person increase the price by a% and again the prices increased by b%, then there is
(
a + b +
ab / 100
)
% increase in profit.
Here, a = 20, b = 20
Using these values in the shortcut, we get:
Net change =
(
20 + 20 +
20x20 / 100
)
% =
(
40 +
400 / 100
)
% = 40 + 4 = 44%
Hence, net increase of 44% in the profit.

49. A shopkeeper marks the prices at 15% higher than the original price. Due to increase in demand, he further increases the price by 10%. How much % profit will he get?
  A.  25.5%
  B.  26.5%
  C.  27.5%
  D.  23.5%
     
   
View Answer

Shortcut:
If a person increase the price by a% and again the prices increased by b%, then there is
(
a + b +
ab / 100
)
% increase in profit.
Here, a = 15, b = 10
Using these values in the shortcut, we get:
Net change =
(
15 + 10 +
15x10 / 100
)
% =
(
25 +
3 / 2
)
% = 25 + 1.5 = 26.5%
Hence, net increase of 26.5% in the profit.

50. The population of a town is decreased by 10% and 20% in two successive years. What per cent population is decreased after two years?
  A.  26%
  B.  24%
  C.  28%
  D.  29%
     
   
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 = 10, b = 20
Using these values in the shortcut, we get:
Net change =
(
− 10 − 20 +
10x20 / 100
)
% =
(
− 30 +
200 / 100
)
% = −30 + 2 = −28%
Hence, net decrease of 28% in the population.

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