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61. Pens are bought at 11 for a rupee and an equal number more at 9 for a rupee. If these are sold at 10 for a rupee, find the loss or gain per cent.
  A.  -2%(-ve sign means loss)
  B.  +1%(+ ve sign means profit)
  C.  -1%(-ve sign means loss)
  D.  -1.5%(-ve sign 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 = 11, k = 9, d = 10
Using these value in shortcut, we get:
Required % profit/loss =
[
(
2 x 11 x 9 / (11 + 9)10
− 1
)
x 100
]
%
=
[
(
2 x 11 x 9 / 20 x 10
− 1
)
x 100
]
%
=
[
(
99 / 100
− 1
)
x 100
]
% =
99 − 100 / 100
x 100% =
−1 x 100 / 100
% = − 1%
Hence, required per cent loss will be 1%.

62. A man bought two oxes for Rs 690. He sold one at a gain of 10% and othe other at a gain of 20% and he found that each ox was sold at the same price. Find the cost prices of the two horses.
  A.  CP of 1st Ox: Rs 380; CP of 2nd Ox: Rs 300
  B.  CP of 1st Ox: Rs 340; CP of 2nd Ox: Rs 370
  C.  CP of 1st Ox: Rs 300; CP of 2nd Ox: Rs 280
  D.  CP of 1st Ox: Rs 360; CP of 2nd Ox: Rs 330
     
   
View Answer

Shortcut:
If a person buys items B and C for Rs Z. He soels B at a gain of a% and the other at a gain of b% and he finds that each tiems B and C is sold at the same price, then the (i) Cost Price of B =
(100 + b) x Z / (100 + a) + (100 + b)

(ii) Cost Price of C =
(100 + a) x Z / (100 + a) + (100 + b)

Here, a = 10, b = 20, Z = 690
Using these value in shortcut, we get:
Cost Price of first ox =
(100 + 20) x 690 / (100 + 10) + (100 + 20)
=
120 x 690 / 110 + 120
=
120 x 690 / 230
= 120 x 3 = 360
Hence, the cost price of first ox is Rs 360.
Cost Price of second ox =
(100 + 10) x 690 / (100 + 10) + (100 + 20)
=
110 x 690 / 110 + 120
=
110 x 690 / 230
= 110 x 3 = 330
Hence, the cost price of second ox is Rs 330.

63. If marbels are bought at the rate of 25 for a rupee, how many must be sold for a rupee so as to gain 25%?
  A.  20
  B.  15
  C.  23
  D.  25
     
   
View Answer

Shortcut:
If certain article is bought at the rate of 'Z' for a rupee, then to a%, the article must be sold at the rate of Selling Price of article =
100 / (100 + a)
x Z
Here, a = 25, Z = 25
Using these value in shortcut, we get:
No. of marbels =
100 / (100 + 25)
x 25 =
100 / 125
x 25 =
100 / 5
= 20
Hence, the 20 marbels will be sold for Re 1.

64. A man buys 5 goats and 7 pigs for Rs 5850. He sells the goats at a profit of 10% and pigs at a profit of 16% and his whole gain is Rs 711. What price does he pay for a goat and a pig?
  A.  Goat price: Rs 680; Pig price: Rs 370
  B.  Goat price: Rs 650; Pig price: Rs 410
  C.  Goat price: Rs 710; Pig price: Rs 320
  D.  Goat price: Rs 790; Pig price: Rs 260
     
   
View Answer

Shortcut:
If a person buys n items of P and m items of Q for Rs Z and sells the items of P at a profit of a% and the items of Q at a profit of b%, and his whole gain is Rs K, then the price he pays for
(i) one items of P =
100K − Zb / n(a − b)

(ii ) one item of Q =
100K − Za / m(b − a)

Here, n = 5, m = 7, Z = 5850, a = 10, b = 16, K = 711
Using these value in shortcut, we get:
Price of goat =
100 x 711 − 5850 x 16 / 5(10 − 16)
=
71100 − 93600 / − 30
=
− 22500 / − 30
= 750
Hence, the price of goat is Rs 750.
Price of pig =
100 x 711 − 5850 x 10 / 7(16 − 10)
=
71100 − 58500 / 7 x 6
12600 / 7 x 6
= 300
Hence, the price of pig is Rs 300.

65. If a man buys 10 pens and 5 pencils for Rs 500, and sells the pens at a profit of 10% and the pencils at a loss of 15%, and his while gain is Rs 25. What price does he pay for a pen and a pencil?
  A.  Pen's price: Rs 30; Pencil's price: Rs 30
  B.  Pen's price: Rs 32; Pencil's price: Rs 28
  C.  Pen's price: Rs 25; Pencil's price: Rs 35
  D.  Pen's price: Rs 40; Pencil's price: Rs 20
     
   
View Answer

Shortcut:
If a person buys n items of P and m items of Q for Rs Z and sells the items of P at a profit of a% and the items of Q at a loss of b%, and his whole gain is Rs K, then the price he pays for
(i) one items of P =
100K + Zb / n(a + b)

(ii ) one item of Q =
Za − 100K / m(a + b)

Here, n = 10, m = 5, Z = 500, a = 10, b = 15, K = 25
Using these value in shortcut, we get:
Price of pen =
100 x 25 + 500 x 15 / 10(10 + 15)
=
2500 + 7500 / 10 x 25
=
10000 / 250
= 40
Hence, the price of pen is Rs 40.
Price of pencil =
500 x 10 − 100 x 25 / 5(10 + 15)
=
5000 − 2500 / 5 x 25
=
2500 / 125
= 20
Hence, the price of pencil is Rs 20.

66. A man buys 5 goats and 7 pigs for Rs 5850. He sells the goats at a loss of 10% and pigs at a loss of 16% and his whole loss is Rs 711. What price does he pay for a goat and a pig?
  A.  Goat's price: Rs 750; Pig's price: Rs 300
  B.  Goat's price: Rs 710; Pig's price: Rs 340
  C.  Goat's price: Rs 680; Pig's price: Rs 370
  D.  Goat's price: Rs 700; Pig's price: Rs 310
     
   
View Answer

Shortcut:
If a person buys n items of P and m items of Q for Rs Z and sells the items of P at a loss of a% and the items of Q at a loss of b%, and his whole loss is Rs K, then the price he pays for
(i) one items of P =
100K − Zb / n(a − b)

(ii ) one item of Q =
Za − 100K / m(a − b)

Here, n = 5, m = 7, Z = 5850, a = 10, b = 16, K = 711
Using these value in shortcut, we get:
Price of goat =
100 x 711 − 5850 x 16 / 5(10 − 16)
=
71100 − 93600 / 5 (− 6)
=
− 22500 / − 30
= 750
Hence, the price of goat is Rs 750.
Price of pig =
5850 x 10 − 100 x 711 / 7(10 − 16)
=
58500 − 71100 / 7(− 6)
=
− 12600 / − 42
= 300
Hence, the price of pig is Rs 300.

67. If a man buys 10 pens and 5 pencils for Rs 500, and sells the pens at a loss of 10% and the pencils at a profit of 15% and his whole loss is Rs 25. What price does he pay for a pen and a pencil?
  A.  Pen's price: Rs 40; Pencil's price: Rs 20
  B.  Pen's price: Rs 40; Pencil's price: Rs 20
  C.  Pen's price: Rs 40; Pencil's price: Rs 20
  D.  Pen's price: Rs 40; Pencil's price: Rs 20
     
   
View Answer

Shortcut:
If a person buys n items of P and m items of Q for Rs Z and sells the items of P at a loss of a% and the items of Q at a profit of b%, and his whole loss is Rs K, then the price he pays for
(i) one items of P =
100K + Zb / n(a + b)

(ii ) one item of Q =
Za − 100K / m(a + b)

Here, n = 10, m = 5, Z = 500, a = 10, b = 15, K = 25
Using these value in shortcut, we get:
Price of pen =
100 x 25 + 500 x 15 / 10(10 + 15)
=
2500 + 7500 / 10 (25)
=
10000 / 250
= 40
Hence, the price of pen is Rs 40.
Price of pencil =
500 x 10 − 100 x 25 / 5(10 + 15)
=
5000 − 2500 / 5(25)
=
2500 / 125
= 20
Hence, the price of pencil is Rs 20.

68. A man bought some pens at a rate of 5 per rupee. He bought the same number of pens at the rate of 4 per rupee. He mixes both the types and sells at 9 for rupees 2. He bears a loss of Rs 3. Find out how many pens he bought in all?.
  A.  1120 pens
  B.  1080 pens
  C.  1000 pens
  D.  1040 pens
     
   
View Answer

Shortcut:
If a person buys n items per rupee and m items per rupee and mixes them in same number ans sells at p items per rupee and bears loss of Rs Z, then number of total items bought is given by
Z x 2nmp / p(n + m) − 2nm

Here, n = 5, m = 4, p = 9/2 or 4.5, Z = 3
Using these value in shortcut, we get:
Price of pen =
3 x 2 x 5 x 4 x 4.5 / 4.5(5 + 4) − 2 x 5 x 4
=
540 / 40.5 − 40
=
540 / 0.5
= 1080
Hence, the he bought 1080 pen.

69. A shopkeeper marks his goods at 25% above his CP and allows buyers a discount of 12
1 / 2
% for cash. Calculate his profit or loss percentage.
  A.  11
5 / 8
% Gain
  B.  9
7 / 3
% Gain
  C.  8
7 / 9
% Gain
  D.  9
3 / 8
% Gain
     
   
View Answer

Shortcut:
If a shopkeeper marks his goods at a% above his cost price and allows buyers a discount of b% for cash, then profit or loss % is given by a − b −
ab / 100
according to +ve or −ve sign respectively.
Here, a = 25, b = 12
1 / 2
or
25 / 2
or 12.5
Using these value in shortcut, we get:
Profit/Loss % = 25 − 12.5 −
25 x 12.5 / 100
= 12.5 −
125 / 40
= 12.5 −
25 / 8
=
100 − 25 / 8
=
75 / 8
= 9
3 / 8

Hence, the profit % is 9
3 / 8
%.

70. A wholeseller allows a discount of 10% for cash payment. How much percent above the cost price must he mark his goods to make a profit of 10%?
  A.  17
3 / 9
%
  B.  20
2 / 7
%
  C.  22
2 / 9
%
  D.  23
2 / 5
%
     
   
View Answer

Shortcut:
These types of questions are solved by the relationship in the following equation
z = a − b −
ab / 100

a = marked percentage above cost price
b = discount in per cent
z = profit in per cent

Here, a = ?, b = 10, z = 10
Using these value in shortcut, we get:
10 = a − 10 −
a x 10 / 100

10 = a − 10 −
a / 10

10 x 10 = 10a − 100 − a
100 = 9a − 100
9a = 200
a =
200 / 9
= 22
2 / 9
%
Hence, the required % is 22
2 / 9
%.

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