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71. The manufacturer of an article makes a profit of 25%, the wholesale dealer makes a profit of 20%, and the retailer makes a profit of 28%. Find the manufacturing price of the article if the retailer sold it for Rs 48.
  A.  Rs 40
  B.  Rs 25
  C.  Rs 35
  D.  Rs 30
     
   
View Answer

Shortcut:
The manufacturere of an article makes a profit of a%, the wholesale dealer makes a profit of b%, and the retailer makes a profit of c%. If the retailer sold it for Rs 'Z' then the manufacturing price of the article is obtained by the Z
(
100 / 100 + a
)
(
100 / 100 + b
)
(
100 / 100 + c
)
.
Here, Z = 48, a = 25, b = 20, c = 28
Using these values in the shortcut, we get:
Price = 48
(
100 / 100 + 25
)
(
100 / 100 + 20
)
(
100 / 100 + 28
)
= 48
(
100 / 125
)
(
100 / 120
)
(
100 / 128
)
=
48 x 100 x 100 x 100 / 125 x 120 x 128
= 25
Hence, manufacturing price of the article is Rs 25.

72. What quantity of water should be added to reduce 9 litres of 50% acidic liquid to 30% acidic liquid?
  A.  8 litres
  B.  2 litres
  C.  6 litres
  D.  5 litres
     
   
View Answer

Shortcut:
In 'Z' litres of a% acidic liquid, the amount of water to be added to make b% acidic liquid is Z
(
a − b / b
)
.
Here, Z = 9, a = 50, b = 30
Using these values in the shortcut, we get:
Added water quantity = 9
(
50 − 30 / 30
)
= 9
(
20 / 30
)
=
9 x 2 / 3
= 6
Hence, 6 litres of water to be added.

73. What quantity of water should be taken out to concentrate 15 litres of 40% acidic liquid to 60% acidic liquid.
  A.  3 litres
  B.  9 litres
  C.  4 litres
  D.  5 litres
     
   
View Answer

Shortcut:
In 'Z' litres of a% acidic liquid, the amount of water to be taken out from the acidic liquid to make b% acidic liquid is Z
(
b − a / b
)
.
Here, Z = 15, a = 40, b = 60
Using these values in the shortcut, we get:
Water quantity = 15
(
60 − 40 / 60
)
= 15
(
20 / 60
)
=
15 / 3
= 5
Hence, 5 litres of water to be taken out.

74. In 1 kg mixture of sand and iron, 20% is iron. How much sand should be added so that the proportion of iron becomes 10%?
  A.  1 kg
  B.  0.5 kg
  C.  2 kg
  D.  1.5 kg
     
   
View Answer

Shortcut:
When a certain quantity of goods Y is added to change, the percentage of goods X in a mixture of X and Y then the quantity of Y to be added is
[
(Previous % value of X) x (Mixture Quantity) / Changed % value of X
− Mixture Quantity
]
.
Here, Previous % value of X = 20, Changed % value of X = 10, Mixture Quantity = 1 kg
Using these values in the shortcut, we get:
Quantity to be added =
[
(Previous % value of X) x (Mixture Quantity) / Changed % value of X
− Mixture Quantity
]
=
[
20 x 1 / 10
− 1
]
= 1 kg
Hence, 1 kg is to be added.

75. In an examination the percentage of students qualified to the number of students appeared from school 'A' is 70%. In school 'B' the number of students appeared is 20% more than the students appeared from school 'A' and the number of students qualified from school 'B' is 50% more than the studetns qualified from school 'A'. What is the percentage of students qualified to the number of students appeared from school 'B'?
  A.  85%
  B.  89.75%
  C.  87.5%
  D.  75.5%
     
   
View Answer

Let 100 students appeared from school A. Then we have
Appeared Passed
A 100 70
B 120 70 + 50% of 70 = 105
Required % =
105 / 120
x 100 = 87.5%

76. Wheat is now being sold at Rs 25 per kg. During last month its cost was Rs 21 per kg. Find by how much per cent a family should reduce it's consumption, so as to keep the expenditure the same.
  A.  Rs 7 per kg
  B.  Rs 4 per kg
  C.  Rs 3 per kg
  D.  Rs 1 per kg
     
   
View Answer

Shortcut:
If the original price of a commodity is Rs A and new price of the commodity is Rs B, then the decrease or increase in consumption so as not to increase or decrease the expenditure respectively, is
(B − A) 100 / B
%
Here, A = 21, B = 25
Using these values in the shortcut, we get:
Required % =
(25 − 21)100 / 25
% =
4 x 100 / 25
% = 16%
Hence, 16% is to be reduced.

77. A reduction of 25% in the price of tea enables person to buy 5 kg more for Rs 120. Find the original price of tea per kg.
  A.  Rs 10 per kg
  B.  Rs 5 per kg
  C.  Rs 6 per kg
  D.  Rs 8 per kg
     
   
View Answer

Shortcut:
If the original price of a commodity is Rs A and the new price of a commodity is Rs B, then keeping expenditure (E) constant, change in quantity of commodity consumed(ΔQ) is obtained by the
E(B − A) / B x A

Here, ΔQ (Change in Quantity consumed) = 4, B − A (Change in price) = 2, E (Expenditure) = 16
Using these values in the shortcut, we get:
4 =
16 x 2 / (A − 2)A

⇒ 4 (A − 2)A = 16 x 2
⇒ (A − 2)A = 8
⇒ A2 − 2A − 8 = 0
⇒ A2 − 4A + 2A − 8 = 0
⇒ A(A − 4) +2(A − 4) = 0
⇒ (A − 4)(A + 2) = 0
∴ Original price of sugar = Rs 4 per kg

78. Split the number 120 into two parts such that one part is 20% of the other.
  A.  80 and 60
  B.  90 and 50
  C.  100 and 20
  D.  95 and 45
     
   
View Answer

Shortcut:
To split a number N into two parts such that one part is a% of the other. The two split parts are
100 / 100+a
x N and
a / 100+a
x N.
Here, N = 120, a = 20
Using these values in the shortcut, we get:
Numbers are
100 / 100 + 20
x 120 and
20 / 100+20
x 120
100 / 120
x 120 and
20 / 120
x 120
100 and 20
Hence, the numbers are 100 and 20

79. 240 litres of oil was poured into a tank and it was still 20% empty. How much oil must be poured into the tank in order to fill it to the brim?
  A.  60 litres
  B.  85 litres
  C.  75 litres
  D.  45 litres
     
   
View Answer

Shortcut:
If A litres of oil was poured into a tank and it was still a% empty. Then the capacity of the tank is
A x 100 / 100 − a

Here, A = 240, a = 20
Using these values in the shortcut, we get:
Required capacity =
240 x 100 / 100 − 20
=
240 x 100 / 80
= 3 x 100 = 300 litres
Hence, the capacity is of 300 litres.

80. 20 litres of a mixture contains 20% alchol and the rest water.If 4 litres of water be mixed in it,the percentage of alchol in the new mixture will be
  A.  33
1 / 3
%
  B.  16
2 / 3
%
  C.  25%
  D.  12
1 / 2
%
     
   
View Answer

In a 20 litres of mixture,

Alcohol =
20 × 20 / 100
= 4 litres

Water = 20 − 4 = 16 litres

On adding 4 litres of water Quantity of water = 16 + 4 = 20 litres

quantity of mixture = 24 litres

∴ Required percentage=
4 / 24
× 100 =
50 / 3
= 16
2 / 3
%

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