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31. The population of a town is 8000. It increases by 10% during the first year and by 20% druing the second year. What will be the population after two years?
  A.  10,560
  B.  10,460
  C.  10,570
  D.  11,560
     
   
View Answer

Shortcut:
The population of a town is P. It increases by a% during the first year, increases by b% during the second year and again increases by c% during the third year. The population after 3 years will be
P x (100+a)(100+b)(100+c) / 100 x 100 x 100

Here, P = 8000, a = 10%, b = 20%
Using these values in the shortcut, we get:
Population will be =
8000 x (100+10)(100+20) / 100 x 100
=
8000 x 110 x 120 / 100 x 100
= 8 x 11 x 120 = 10560
Hence, the population will be 10560 of the town.

32. The population of a town is 10,000. It increases by 10% during the first year. During the second year, it decreases by 20% and increased by 30% during the third year. What will be the population after 3 years?
  A.  11,340
  B.  11,540
  C.  10,440
  D.  11,440
     
   
View Answer

Shortcut:
The population of a town is P. It increases by a% during the first year, decreases by b% during the second year and again increases by c% during the third year. The population after 3 years will be
P x (100+a)(100−b)(100+c) / 100 x 100 x 100

Here, P = 10000, a = 10%, b = 20%, c = 30%
Using these values in the shortcut, we get:
Population will be =
10000 x (100+10)(100−20) (100+30) / 100 x 100 x 100
=
10000 x 110 x 80 x 130 / 100 x 100 x 100
= 11 x 8 x 130 = 11440
Hence, the population will be 11440 of the town.

33. During one year, the population of a locality increases by 5% but during the next year, it decreases by 5%. If the population at the end of the second year was 7980, find the population at the beginning of the first year.
  A.  7,000
  B.  8,100
  C.  8,000
  D.  9,000
     
   
View Answer

Shortcut:
If during the first year, the population of a town increases by a%, decreases by b% during the second year and again decreases by c% during the third year and the population after 3 years will be P. Then the population at the beginning of the first year was
P x 100 x 100 x 100 / (100 + a)(100 − b)(100 − c)

Here, P = 7980, a = 5%, b = 5%,
Using these values in the shortcut, we get:
Population will be =
7980 x 100 x 100 / (100 + 5)(100 − 5)
=
7980 x 100 x 100 / 105 x 95
=
7980 x 100 x 4 / 21 x 19
= 20 x 100 x 4 = 8000
Hence, the population was 8000 of the town.

34. The population of a town increases at the rate of 10% during one year and it decreases at the rate of 10% during the second year. If it has 29,700 inhabiants at present, find the number of inhabitants two years ago.
  A.  30,100
  B.  30,000
  C.  31,000
  D.  32,000
     
   
View Answer

Shortcut:
If during the first year, the population of a town increases by a%, decreases by b% during the second year and again decreases by c% during the third year and the population after 3 years will be P. Then the population at the beginning of the first year was
P x 100 x 100 x 100 / (100 + a)(100 − b)(100 − c)

Here, P = 29700, a = 10%, b = 10%,
Using these values in the shortcut, we get:
Population will be =
29700 x 100 x 100 / (100 + 10)(100 − 10)
=
29700 x 100 x 100 / 110 x 90
=
297 x 100 x 100 / 11 x 9
= 30 x 100 x 100 = 30000
Hence, the inhabitants were 30000 of the town.

35. The population of a town increases by 10% during the first year and by 20% during the second year. The present population of a town is 26400. Find the population of the town two years ago.
  A.  20,000
  B.  21,000
  C.  18,000
  D.  22,000
     
   
View Answer

Shortcut:
The population of a town increases by a% in first year, increases by b% during the second year and again increases by c% during the third year and if the present population of a town is P, then the population three years ago was
P x 100 x 100 x 100 / (100 + a)(100 + b)(100 + c)

Here, P = 26400, a = 10%, b = 20%,
Using these values in the shortcut, we get:
Population will be =
26400 x 100 x 100 / (100 + 10)(100 + 20)
=
26400 x 100 x 100 / 110 x 120
=
264 x 100 x 100 / 11 x 12
= 2 x 100 x 100 = 20000
Hence, the population was 20000 of the town.

36. The population of a town is 8000. It decreases by 10% during the first year, 15% during the second year and 20% during the third year. What will be the population after 3 years?
  A.  4,996
  B.  5,896
  C.  4,796
  D.  4,896
     
   
View Answer

Shortcut:
The population of a town is P. It decreases by a% in first year, decreases by b% during the second year and again decreases by c% during the third year. The population of a town after three years will be
P x (100 − a)(100 − b)(100 − c) / 100 x 100 x 100

Here, P = 8000, a = 10%, b = 15%, c = 20%
Using these values in the shortcut, we get:
Population will be =
8000 x (100 − 10)(100 − 15)(100 − 20) / 100 x 100 x 20
=
8000 x 90 x 85 x 80 / 100 x 100 x 100
=
8 x 9 x 85 x 8 / 10
= 8 x 9 x 17 x 4 = 4896
Hence, the population will be 4896 of the town.

37. The population of a town decreases by 20% during the first year, decreases by 30% during the second year and again decreases by 40% during the third year. If the present population of the town is 67200 then what was the population of the town three years ago?
  A.  3,00,000
  B.  2,00,000
  C.  1,00,000
  D.  3,10,000
     
   
View Answer

Shortcut:
The population of a town decreases by a% in first year, decreases by b% during the second year and again decreases by c% during the third year. If the present population of a town is P, then the population of the town, three years ago was
P x (100 − a)(100 − b)(100 − c) / 100 x 100 x 100

Here, P = 67200, a = 20%, b = 30%, c = 40%
Using these values in the shortcut, we get:
Population will be =
67200 x 100 x 100 x 100 / (100 − 20)(100 − 30)(100 − 40)
=
67200 x 100 x 100 x 100 / 80 x 70 x 60
=
672 x 10 x 100 x 100 / 8 x 7 x 6
= 2 x 10 x 100 x 100 = 200000
Hence, the population was 200000 of the town.

38. The population of a town is 8000. if the males increase by 6% and the females by 10%, the population will be 8600. Find the number of females.
  A.  3,100
  B.  2,000
  C.  3,000
  D.  3,300
     
   
View Answer

Shortcut:
The population of a town is P1. If the males increases by a% and the females by b% , the population becomes P2, then the number of males and females are given by
P2 x 100 − P1(100 + b) / a − b
and
P2 x 100 − P1(100 + a) / b − a
respectively.
Here, P1 = 8000, a = 6%, b = 10%, P2 = 8600
Using these values in the shortcut, we get:
Female Population =
8600 x 100 − 8000(100 + 6) / 10 − 6
=
8600 x 100 − 8000 x 106 / 4
=
860000 − 848000 / 4
=
12000 / 4
= 3000
Hence, the population of females is 3000.

39. If the price of a commodity be raised by 20%, find by how much per cent must a householder reduce his consumption of that commodity so as not to increase his expenditure.
  A.  15
2 / 3
%
  B.  17
2 / 3
%
  C.  18
2 / 3
%
  D.  16
2 / 3
%
     
   
View Answer

Shortcut:
If the price of a comodity increases by a%, then the reduction in consumption so as not to increase the expenditure, is
a / 100 + a
x 100%
Here, a = 20%
Using these values in the shortcut, we get:
Reduction % =
20 / 100 + 20
x 100% =
20 / 120
x 100% =
1 / 6
x 100% =
50 / 3
% = 16
2 / 3
%
Hence, reduction will be 16
2 / 3
%.

40. If the price of sugar falls down by 10%, by how much per cent must a householder increase its consumption, so as not to decrease expenditure in this item?
  A.  12
1 / 9
%
  B.  11
1 / 9
%
  C.  10
1 / 9
%
  D.  11
1 / 7
%
     
   
View Answer

Shortcut:
If the price of a comodity decreases by a%, then the increase in consumption so as not to increase the expenditure, is
a / 100 − a
x 100%
Here, a = 10%
Using these values in the shortcut, we get:
Increment % =
10 / 100 − 10
x 100% =
10 / 90
x 100% =
1 / 9
x 100% =
100 / 9
% = 11
1 / 9
%
Hence, increment will be 11
1 / 9
%.

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