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41. A man sells pulses at a profit of 5%. If he reduces the price by Rs 4 per kg, he would make a loss of 15%. Find the cost price and the initial selling price per kg of pulses.
  A.  Cost price: Rs 25; Selling price : Rs 27
  B.  Cost price: Rs 20; Selling price : Rs 21
  C.  Cost price: Rs 15; Selling price : Rs 30
  D.  Cost price: Rs 30; Selling price : Rs 25
     
   
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Shortcut:
A person sells an article at a profit of a%. If he reduces the price by Rs 'Z', he would incur loss of b%, then the cost price and the initial selling price of the article are Rs
Z x 100 / a + b
and Rs
Z(100 + a) / a + b
respectively.
Here, a = 5, b = 15, Z = 4
Using these value in shortcut, we get:
Initial Cost Price = Rs
Z x 100 / a + b
= Rs
100 x 4 / 5 + 15
= Rs
100 x 4 / 20
= 5 x 4 = Rs 20
Hence, cost price of pulses be Rs 20 per kg. Selling Price = Rs
Z(100 + 5) / a + b
= Rs
4 x 105 / 5 + 15
= Rs
4 x 105 / 20
= 21
Hence, selling price of pulses be Rs 21 per kg.

42. A vendor sells coconut at a profit of 40%. If he reduces the selling price of each orange by 30 paise, he earns a profit of 25%. Find the cost price and the initial selling price of each coconut.
  A.  Cost price: 200 Paise; Selling price: 280 paise
  B.  Cost price: 180 Paise; Selling price: 230 paise
  C.  Cost price: 210 Paise; Selling price: 240 paise
  D.  Cost price: 250 Paise; Selling price: 210 paise
     
   
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Shortcut:
A person sells an article at a profit of a%. If he reduces the price by Rs 'Z', he makes profit of b%, then the cost price and the initial selling price of the article are Rs
Z x 100 / a − b
and Rs
Z(100 + a) / a − b
respectively.
Here, a = 40, b = 25, Z = 30 paise
Using these value in shortcut, we get:
Initial Cost Price = Rs
Z x 100 / a − b
= Rs
30 x 100 / 40 − 25
= Rs
100 x 30 / 15
= 100 x 2 = 200 paise
Hence, cost price of pulses be 200 paise. Selling Price = Rs
30(100 + 40) / a − b
= Rs
30 x 140 / 40 − 25
= Rs
30 x 140 / 15
= 280 paise
Hence, selling price of pulses be Rs 280 paise.

43. An article is sold at 20% profit. If its cost price and selling price are less by Rs 10 and Rs 5 respectively and the percentage profit increases by 10%. Find the cost price.
  A.  Rs 90
  B.  Rs 60
  C.  Rs 50
  D.  Rs 80
     
   
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Shortcut:
An article is sold at a% profit. If its cost price is lowered by Rs m and at the same time its selling price is also lowered by Rs n, and the percentage of profit increases by b%. Then the cost price of that article is given by Rs
m (a + b) − 100(n −m) / b
.
Here, a = 20, m = 10, n = 5, b = 10 paise
Using these value in shortcut, we get:
Cost Price = Rs
10(20 + 10) − 100(5 − 10) / 10
= Rs
300 + 500 / 10
= Rs
800 / 10
= Rs 80
Hence, cost price of the article be Rs 80.

44. An article is sold at 25% profit. If its CP and SP are increased by Rs 20 and Rs 4 respectively, the percentage of profit decreases by 15%. Find the cost price.
  A.  Rs 110
  B.  Rs 95
  C.  Rs 120
  D.  Rs 100
     
   
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Shortcut:
An article is sold at a% profit. If its cost price and selling price are increased by Rs m and Rs n respectively and the percentage profit decreases by b%, then the cost price of that article is given by Rs
m (a − b) − 100(n −m) / b
.
Here, a = 25, m = 20, n = 4, b = 15 paise
Using these value in shortcut, we get:
Cost Price = Rs
20(25 − 15) − 100(4 − 20) / 15
= Rs
200 + 1600 / 15
= Rs
1800 / 15
= Rs 120
Hence, cost price of the article be Rs 120.

45. A man sells his table at a profit of 12
1 / 2
% and the chair at a loss of8
1 / 3
% but on the whole he gains Rs 25. On the other hand if he sells the table at a loss of8
1 / 3
% and the chair at a profit of 12
1 / 2
% then he neither gains nor loses. Find the cost price of the table and the chair.
  A.  Table Cost Price: Rs 320; Chair's cost price: Rs 200
  B.  Table Cost Price: Rs 360; Chair's cost price: Rs 240
  C.  Table Cost Price: Rs 300; Chair's cost price: Rs 210
  D.  Table Cost Price: Rs 290; Chair's cost price: Rs 300
     
   
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Shortcut:
If a person sells an item 'A' at a profit of a1% and the other item 'B' at a loss of b1%, but on the whole he gains Rs Z. On the other hand if he sells the item 'A' at a loss of b2% and the item 'B' at a profit of a2%, then he neither gains nor loses, then the (i) Cost price of A is Rs
Z x a1 / a1xa2 − b1 x b2
x 100
(ii) The cost price of B is Rs
Z x b1 / a1xa2 − b1xb2
x 100.
Here, a1 = 12
1 / 2
or
25 / 2
, b1 = 8
1 / 3
or
25 / 3
, a2 = 12
1 / 2
or
25 / 2
, b2 = 8
1 / 3
or
25 / 3
, Z = 25
Using these value in shortcut, we get:
Cost Price of table = Rs
25 x 25/2 / (25/2 x 25/2) − (25/3 x 25/3)
x 100 = Rs 360
Hence, cost price of the table be Rs 360. Cost Price of chair = Rs
25 x 25/3 / (25/2 x 25/2) − (25/3 x 25/3)
x 100 = Rs 240
Hence, cost price of the table be Rs 240.

46. The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit per cent.
  A.  12
3 / 7
%
  B.  11
5 / 3
%
  C.  11
1 / 9
%
  D.  9
2 / 9
%
     
   
View Answer

Shortcut:
If cost price of a articles is equal to the selling price of b articles, then the profit percentage will be
a − b / b
x 100 %

Here, a = 10, b = 9
Using these value in shortcut, we get:
Profit % =
10 − 9 / 9
x 100 =
1 / 9
x 100 = 11
1 / 9
%
Hence, profit % will be 11
1 / 9
%.

47. An article is sold at 20% profit. If its cost price is increased by Rs 50 and at the same time if its selling price is also increased by Rs 30, the percentage of profit becomes 16
2 / 3
%. Find the cost price.
  A.  Rs 870
  B.  Rs 800
  C.  Rs 830
  D.  Rs 850
     
   
View Answer

Shortcut:
An article is sold at a% profit. If its cost price is increased by Rs M and at the same time if its selling price is also increased by Rs N, the percentage profit becomes b%, then the cost price of the article is Rs
M − N + (Mb/100) / a − b
x 100
Here, a = 20, b = 16
2 / 3
or
50 / 3
, M = 50, N = 30
Using these value in shortcut, we get:
Cost Price =
50 − 30 + (50 x 50/3)/100 / 20 − 50/3
x 100
=
20 + (50 x 50)/300 / 10/3
x 100
=
20 + 25/3 / 10/3
x 100
=
85/3 / 10/3
x 100 =
85 x 3 / 3 x 10
x 100 = 8.5 x 100 = 850
Hence, cost price will be Rs 850.

48.
1 / 3
of a commodity is sold at 15% profit,
1 / 4
is sold at 20% profit and the rest at 24% profit. If the total profit of Rs 62 is earned, then find the value of the commodity.
  A.  Value: Rs 325
  B.  Value: Rs 310
  C.  Value: Rs 298
  D.  Value: Rs 320
     
   
View Answer

Shortcut:
If 'm' part is sold at a% profit, 'n' part is sold at b% profit, 'q' part is sold at c% profit and Rs 'P' is earned as overall profit then the value of total consignment is Rs
P x 100 / ma + nb + qc
, (Where m + n + q = total)
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.

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

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

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

50. A man bought two watches for Rs 480. He sold one at a loss of 15% and the other at a gain of 19% and he found that each watch was sold at the same price. Find the cost prices of the two watches.
  A.  Rs 180
  B.  Rs 220
  C.  Rs 200
  D.  Rs 240
     
   
View Answer

Shortcut:
If a person bought two items for Rs Z. He sold one at loss of a% and the other at a gain of b% and he found that each item was sold at the same price, thenthe cost prices of two items are (i) Cost price of the item sold at loss is Rs
Z x (100 + b) / (100 − a) + (100 + b)

(ii) Cost price of the item sold at gain is Rs
Z x (100 − a) / (100 − a) + (100 + b)

Here, Z = 480, a = 15, b = 19
Using these value in shortcut, we get:
Cost price of watches sold at loss =
480 x (100 + 19) / (100 − 15) + (100 + 19)
=
480 x 119 / 85 + 119
=
480 x 119 / 204
= 280
Hence, the cost price of watches sold at loss will be Rs 280.
Cost price of watches sold at gain =
480 x (100 − 15) / (100 − 15) + (100 + 19)
=
480 x 85 / 85 + 119
=
480 x 85 / 204
= Rs 200
Hence, the cost price of watches sold at gain will be Rs 200.

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