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81. 120 litres of oil was poured into a tank and it was still 60% empty. Find the capacity of the tank.
  A.  300 litres
  B.  100litres
  C.  400 litres
  D.  250 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 = 120, a = 60
Using these values in the shortcut, we get:
Required capacity =
120 x 100 / 100 − 60
=
120 x 100 / 40
= 3 x 100 = 300
Hence, the capacity is of 300 litres.

82. Find a single equivalent increase, if a number is sucessively increased by 10%, 15% and 20%.
  A.  50 %
  B.  51.8%
  C.  48.25%
  D.  52.15%
     
   
View Answer

Shortcut:
If a number is successevely increased by a%, b% and c%, then single equivalent increase in that number will be
[
(a + b + c) +
(
ab + bc + ca / 100
)
+
(
abc / (100)2
)
]
%
Here, a = 10, b = 15, c = 20
Using these values in the shortcut, we get:
Required increase % =
[
(10 + 15 + 20) +
(
10x15 + 15x20 + 20x10 / 100
)
+
(
10x15x20 / (100)2
)
]
%
=
[
45 +
(
150 + 300 + 200 / 100
)
+
(
3000 / 100 x 100
)
]
%
=
[
45 +
650 / 100
+
3000 / 100 x 100
]
%
= [45 + 6.5 + 0.3]% = 51.8%

83. Find a single discount equivalent to a discount series of 20%, 10% and 5%.
  A.  21.4%
  B.  31.6%
  C.  33.84%
  D.  41.15%
     
   
View Answer

Shortcut:
If three successive discounts of a%, b% and c%, are allowed on an amount then a single discount that equivalent to the three successive discounts will be
[
(a + b + c) −
(
ab + bc + ca / 100
)
−
(
abc / (100)2
)
]
%
Here, a = 20, b = 10, c = 5
Using these values in the shortcut, we get:
Required % =
[
(20 + 10 + 5) −
(
20x10 + 10x5 + 5x20 / 100
)
−
(
20x10x5 / (100)2
)
]
%
=
[
35 −
(
200 + 50 + 100 / 100
)
−
(
1000 / 100 x 100
)
]
%
=
[
35 −
(
350 / 100
)
−
(
1000 / 100 x 100
)
]
%
= [35 − 3.5 − 0.1]% = [35 − 3.4]% = 31.6%

84. The price of sugar is decreased by 20% and its consumption increases by 30%. Find the new expenditure as a ratio of initial expenditure.
  A.  26:25
  B.  21:25
  C.  10:15
  D.  25:10
     
   
View Answer

Shortcut:
The price of commodity is decreased by a% and its consumption increases by b%. The new expenditure as a ratio of initial expenditure is given by
New expenditure / Initial expenditure
=
(100 + a)(100 + b) / (100)2

[Note: Put a & b as (+a) & (+b), in the case of increase and (-a) & (-b), in the case of decrease.]
Here, a = −20, b = 30
Using these values in the shortcut, we get:
Required ratio =
(100 − 20)(100 + 30) / (100)2

=
80 x 130 / 100 x 100
=
8 x 13 / 100
=
104 / 100
=
26 / 25

Hence, the ratio of initial expenditure is 26 : 25

85. In an examination 30% of the students failed in Maths 25% of the students failed in English, 40% of the students failed in Hindi. If 15% of the students failed in Maths and English, 20% of the studetns failed in English and hindi, 25% of the students failed in Maths and Hindi and 10% of the students failed in all the three subjects Maths, English and Hindi, then find the percentage of students who passed in all three subjects.
  A.  58%
  B.  55%
  C.  51%
  D.  49%
     
   
View Answer

Shortcut:
(A∪B∪C) = n(A) + n(B) + n(C) − n(A∪B) − n(B∩C) − n(A∩C) + n(A∩B∩C)
∴ Total per cent of failed candidates = 30 + 40 + 25 − 25 − 20 − 15 + 10 = 45%
∴ Total per cent of passed candidates = 100 − 45 = 55%

86. In a recent survey 25% houses contained tow or more people. Of those houses containing only one person 20% were having only a male. What is the percentage of all houses which contain exactly one female and no males?
  A.  60%
  B.  55%
  C.  63%
  D.  58%
     
   
View Answer

Shortcut:
In a recent survey a% houses contained two or more people. Of those houses containing only one person b% were having only a male. The percentage of all houses which contain exactly one female and no males is given by
(100 − a)(100 − b) / 100
%
Here, a = 25, b = 20
Using these values in the shortcut, we get:
Required % =
(100 − 25)(100 − 20) / 100
% =
75 x 80 / 100
% =
3 x 80 / 4
% = (3 x 20)% = 60%
Hence, the percentage is 60%.

87. Ram's monthly income is 15% more than that of Shyam. Shyam's monthly income is 10% less than that of Sohan. If the difference between the montly incomes of Ram and Sohan is Rs 350, what is the monthly income of Shyam?
  A.  Shyam's Income: Rs 6,000; Sohan's Income: Rs 7,000
  B.  Shyam's Income: Rs 10,000; Sohan's Income: Rs 9,000
  C.  Shyam's Income: Rs 4,000; Sohan's Income: Rs 7,000
  D.  Shyam's Income: Rs 9,000; Sohan's Income: Rs 10,000
     
   
View Answer

Shortcut:
Monthly income of Q is a% more tha that of R. Monthly income of R is b% less than that of S. If the difference between the monthy incomes of Q and S is Rs 'Z', then the monthly incomes of R and S are given by Rs
100 x (100 − b) x Z / (100 + a)(100 − b) − (100)2
and Rs
(100)2 x Z / (100 + a)(100 − b) − (100)2

Here, a = 15, b = 10, Z = 350

Using these values in the shortcut, we get:

Shyam's income =
100 x (100 − 10) x 350 / (100 + 15)(100 − 10) − (100)2
=
(100 x 90) x 350 / (115)(90) − (10000)
=
9000 x 350 / (10350) − (10000)
= Rs 9000

Hence, Shyam's income is Rs 9,000.

Sohan's income = Rs
100x100 x 350 / (100 + 15)(100 − 10) − (100)2
=
100 x 100 x 350 / (115)(90) − (10000)
=
100 x 100 x 350 / (10350) − (10000)
=
100 x 100 x 350 / 350
= 100 x 100 = 10000

Hence, Sohan's income is Rs 10,000.

88. Weight of two persons A and B are in the ratio of 3:5. A's weight increases by 20% and the total weights of A and B together becomes 80 kg, with an increase of 25%. By what per cent did the weight of B increase?
  A.  32%
  B.  25%
  C.  28%
  D.  22%
     
   
View Answer

Shortcut:
Weights of two persons Q and R are in the ratio of q:r. Q's weight increases by a% and the total weight of Q and R together becomes 'Z'kg, with an increase of b%, then the percentage increase in the weight of R is given by
[
(
100 + b / 100
)
(
1 +
q / r
)
−
{
q / r
(
100 + a / 100
)
+ 1
}
]
x 100%
Here, a = 20, b = 25, q = 3, r = 5
Using these values in the shortcut, we get:
[
(
100 + 25 / 100
)
(
1 +
3 / 5
)
−
{
3 / 5
(
100 + 20 / 100
)
+ 1
}
]
x 100%

=
[
(
125 / 100
)
(
1 +
3 / 5
)
−
{
3 / 5
(
120 / 100
)
+ 1
}
]
x 100%

=
[
(
125 / 100
)
(
8 / 5
)
−
{
3 x 120 / 5 x 100
+ 1
}
]
x 100%

=
100 − 86 / 50
x 100 = 28%

89. Raj spends 20% of his monthly income on food and 25% of the remaining on room rent. He saves the remaining amount. If the saving amount is Rs 6000, find the monthly income of Raj, the amount spent on food and the amount spent on room rent.
  A.  Raj's monthly income: Rs 12,000; Amount spent on food: Rs 5000; Amount spent of room rent: Rs 3000
  B.  Raj's monthly income: Rs 10,000; Amount spent on food: Rs 2000; Amount spent of room rent: Rs 2000
  C.  Raj's monthly income: Rs 9,000; Amount spent on food: Rs 3000; Amount spent of room rent: Rs 6000
  D.  Raj's monthly income: Rs 2,000; Amount spent on food: Rs 10,000; Amount spent of room rent: Rs 1000
     
   
View Answer

Shortcut:
A person spends a% of his monthy income on item 'Q' and b% of the remaining on the item 'R'. He saves the remaining amount. If the saving amount is Rs 'W', then
(i) the monthy income of the person = Rs
W x (100)2 / (100 − a)(100 − b)

(ii) the monthly amount spent on the item Q = Rs
W x a x 100 / (100 − a)(100 − b)

(iii) the monthly amount spent on the item R = Rs
b x W / (100 − b)

Here, a = 20, b = 25, W = 6000
Using these values in the shortcut, we get:
(i) the monthy income of Raj = Rs
6000 x (100)2 / (100 − 20)(100 − 25)
=
6000 x (100) x 100 / (80)(75)
= 1000 x 10 = 10000
(ii) the monthly amount spent on food = Rs
6000 x 20 x 100 / (100 − 20)(100 − 25)
=
6000 x 20 x 100 / (80)(75)
= 2000
(iii) the monthly amount spent on room rent = Rs
25 x 6000 / (100 − 25)
=
25 x 6000 / 75
= 2000

90. When the price of tea was increased by 25%, a family reduced its consumption in such a way that the expenditure on tea was only 20% more than before. If 25 kg were consumed per month before, find the new monthly consumption.
  A.  24 kg
  B.  14 kg
  C.  20 kg
  D.  26 kg
     
   
View Answer

Shortcut:
When the price of an item was increased by a%, a family reduced its consumption in such a way that the expenditure on the item was only b% more than before. If 'Q' kg were consumed per month before, then the new monthly consumption is given by
(
100 + b / 100 + a
)
Q kg
Here, a = 25, b = 20, Q = 25
Using these values in the shortcut, we get:
(
100 + 20 / 100 + 25
)
x 25 =
(
120 / 125
)
x 25 =
24 / 25
x 25 = 24 kg

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