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51. Nadim purchased 20 dozen pens at Rs 48 per dozen. He sold 8 dozen at 10% profit and the remaining 12 dozen at 20% profit. What is his profit percentage in this transaction?
  A.  16%
  B.  12%
  C.  17%
  D.  10%
     
   
View Answer

Shortcut:
A person buys certain quantity of an article for Rs Z. If he sells qth part of the stock at a profit of a% and the remaining rth part at b%, profit, then the percent profit in this trade will be Profit % =
qa + rb / q + r

Here, q = 8, a = 10, r = 12, b = 20
Using these value in shortcut, we get:
Profit % =
(8 x 10) + (12 x 20) / 8 + 12
=
80 + 240 / 20
=
320 / 20
= 16%
Hence, the profit % will be 16%.

52.
1 / 3
of a commodity is sold at 15% loss,
1 / 4
is sold at 20% loss and the rest at 24% loss. If a total loss is Rs 62, then find the value of the commodity.
  A.  Rs 290
  B.  Rs 310
  C.  Rs 325
  D.  Rs 350
     
   
View Answer

Shortcut:
If 'm' part is sold at a% loss, 'n' part is sold at b% loss, the rest part 'q' is sold at c% loss and Rs 'P' is overall loss, then the value of total commodity is Rs
P x 100 / ma + nb + qc

Here, m =
1 / 3
, a = 15, n =
1 / 4
, b = 20, q = (1 −
1 / 3
−
1 / 4
) =
5 / 12
c = 24, P = 62
Using these value in shortcut, we get:
Value of commodity =
62 x 100 / (1/3 x 15) + (1/4 x 20) + (5/15 x 24)
=
62 x 100 / 5 + 5 + 10
=
62 x 100 / 20
= 62 x 5 = 310
Hence, value of commodity will be Rs 310.

53.
2 / 3
of a consignment was sold at 6% loss and the rest at a profit of 3%. If there was an overall loss of Rs 540, find the value of the consignment.
  A.  Rs 19,000
  B.  Rs 15,000
  C.  Rs 18,000
  D.  Rs 21,000
     
   
View Answer

Shortcut:
If 'm' part is sold at a% loss, the rest part 'n' is sold at b% profit, and Rs 'P' is earned as overall loss then the value of total consignment is Rs
P x 100 / ma − nb

Here, m =
2 / 3
, a = 6, n =
(
1 −
2 / 3
)
=
1 / 3
, b = 3, P = 540
Using these value in shortcut, we get:
Value of consignment =
540 x 100 / (2/3 x 6) − (1/3 x 3)
=
540 x 100 / 4 − 1
=
540 x 100 / 3
= 180 x 100 = 18000
Hence, value of commodity will be Rs 18,000.

54. If goods be purchased for Rs 450, and
1 / 3
of it be sold at a loss of 10%, at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
  A.  41%
  B.  29%
  C.  35%
  D.  25%
     
   
View Answer

Shortcut:
A person buys certain quantity of an article for Rs Z. If he sells 'm' part is at a% loss, then to make an overall profit of b%, on the total transaction he should sell the remaining stock at the per cent profit of
b + am / 1 − m
%
Here, m =
1 / 3
, a = 10, b = 20
Using these value in shortcut, we get:
Required % profit =
20 + (10 x 1/3) / 1 − 1/3
=
20 + 10/3 / 2/3
=
70 / 2
= 35%
Hence, required per cent profit will be 35%.

55. A man buys rice for Rs 4400. He sells
1 / 3
rd of it at a profit of 5%. At what percent gain should he sell the remaining
2 / 3
rd so as to make an overall profit of 10% on the whole transaction?
  A.  12
1 / 2
%
  B.  9
3 / 2
%
  C.  13
4 / 7
%
  D.  15
3 / 5
%
     
   
View Answer

Shortcut:
A person buys certain quantity of an article for Rs Z. If he sells 'm' part is at a% profit, then to make an overall profit of b% on the total transaction, he should sell the remaining stock at the per cent profit of
b − am / 1 − m
%
Here, m =
1 / 3
, a = 5, b = 10
Using these value in shortcut, we get:
Required % profit =
10 − (5 x 1/3) / 1 − 1/3
=
10 − 5/3 / 2/3
=
25 / 2
= 12
1 / 2
%
Hence, required per cent profit will be 12
1 / 2
%.

56. A distributor buys books for Rs 8000 from a publisher. he had to sell
1 / 4
th at a loss of 20%. At what percent gain he should sell the remaining stock so as to make an overall no profit no loss on the total transaction?
  A.  7
4 / 3
%
  B.  9
7 / 5
%
  C.  5
2 / 3
%
  D.  6
2 / 3
%
     
   
View Answer

Shortcut:
A person buys certain quantity of an article for Rs Z. If he sells 'm' part is at a% loss, then to make an overall no profit no loss on the total transaction, he should sell the remaining stock at the per cent profit of
am / 1 − m
%
Here, m =
1 / 4
, a = 20
Using these value in shortcut, we get:
Required % profit =
(20 x 1/4) / 1 − 1/4
=
5 / 3/4
=
5 x 4 / 3
=
20 / 3
% = 6
2 / 3
%
Hence, required per cent profit will be 6
2 / 3
%.

57. A man buys rice for Rs 4400. He sells
1 / 3
rd of it at a profit of 5%. At what percent loss should he sell remaining
2 / 3
rd so as to make no profit no loss on the whole transaction?
  A.  2
1 / 2
%
  B.  4
3 / 2
%
  C.  1
3 / 2
%
  D.  4
5 / 2
%
     
   
View Answer

Shortcut:
A person buys certain quantity of an article for Rs Z. If he sells 'm' part is at a% profit, then to make an overall no profit no loss on the total transaction, he should sell the remaining stock at the per cent loss of
am / 1 − m
%
Here, m =
1 / 3
, a = 5
Using these value in shortcut, we get:
Required % profit =
5 x 1/3 / 1 − 1/3
=
5/3 / 2/3
=
5 x 3 / 2 x 3
=
5 / 2
= 2
1 / 2
%
Hence, required per cent loss will be 2
1 / 2
%.

58. A man buys 400 coconut at 4 a rupee and 500 coconut at 2 a rupee. He mixes them togehter and sells them at 3 a rupee. Find his percent loss or gain.
  A.  -14
2 / 7
% (-ve means loss)
  B.  -11
3 / 5
% (-ve means loss)
  C.  -14
7 / 4
% (-ve means loss)
  D.  -13
2 / 7
% (-ve means loss)
     
   
View Answer

Shortcut:
A person buys y articles at m per rupee and z articles at n per rupee. He mixes them together and sells them at b per rupee. Then his gain or loss per cent is
[
(
(y + z)mn / (yn + zm)b
− 1
)
x 100
]
% according as the +ve or −ve sign respectively.
Here, y = 400, m = 4, z = 500, n = 2, b = 3
Using these value in shortcut, we get:
Required profit/loss % =
[
(
(400 + 500)4 x 2 / (400 x 2 + 500 x 4)3
− 1
)
x 100
]
%
=
[
(
900 x 4 x 2 / (800 + 2000)3
− 1
)
x 100
]
%
=
[
(
900 x 4 x 2 / 2800 x 3
− 1
)
x 100
]
%
=
[
(
3 x 2 / 7
− 1
)
x 100
]
% =
[
(
6 / 7
− 1
)
x 100
]
% =
[
(
6 − 7 / 7
)
x 100
]
% =
− 7 / 100
= − 14
2 / 7
%
Hence, required per cent loss will be − 14
2 / 7
%.

59. A man purchases a certain number of mangoes at 3 per rupee and the same number at 4 per rupee. He mixes them togehter and sells them at 3 per rupee. What is his gain or loss percent?
  A.  +17
5 / 2
% (+ means gain)
  B.  +14
2 / 7
% (+ means gain)
  C.  +12
3 / 5
% (+ means gain)
  D.  +9
5 / 2
% (+ means gain)
     
   
View Answer

Shortcut:
A person buys certain number articles at q a rupee and the same number of articles at k a rupee. He mixes them together and sells them at d a rupee. Then his gain or loss per cent is
[
(
2qk / (q + k)d
− 1
)
x 100
]
%
[Note: gain or loss will be reprsented by +ve or -ve sign respectively]
Here, q = 3, k = 4, d = 3
Using these value in shortcut, we get:
Required % profit/loss =
[
(
2 x 3 x 4 / (3 + 4)3
− 1
)
x 100
]
%
=
[
(
2 x 3 x 4 / 7 x 3
− 1
)
x 100
]
%
=
[
(
8 / 7
− 1
)
x 100
]
%
=
1 / 7
x 100% =
100 / 7
% = 14
2 / 7
%
Hence, required per cent profit will be 14
2 / 7
%.

60. A man purchases a certain number of toffees at 25 a rupee and the same number at 20 a rupee. he mixes them together and sells them at 45 for 2 rupees. What does he gain or lose percent in the transaction?
  A.  -1
13 / 85
% (-ve means loss)
  B.  − 1
81 / 19
% (−ve means loss)
  C.  − 1
15 / 77
% (−ve means loss)
  D.  −1
19 / 81
% (−ve means loss)
     
   
View Answer

Shortcut:
A person buys certain number articles at q a rupee and the same number of articles at k a rupee. He mixes them together and sells them at d a rupee. Then his gain or loss per cent is
[
(
2qk / (q + k)d
− 1
)
x 100
]
%
[Note: gain or loss will be reprsented by +ve or -ve sign respectively]
Here, q = 25, k = 20, d =
45 / 2

Using these value in shortcut, we get:
Required % profit/loss =
[
(
2 x 25 x 20 / (25 + 20)45/2
− 1
)
x 100
]
%
=
[
(
2 x 25 x 20 x 2 / 45 x 45
− 1
)
x 100
]
%
=
[
(
2000 / 2025
− 1
)
x 100
]
%
=
2000 − 2025 / 2025
x 100%
=
− (25 x 100) / 2025
%
= −
100 / 81
% = − 1
19 / 81
%
Hence, required per cent loss will be 1
19 / 81
%.

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