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31. A person sells an article at a profit of 10%. If he had bought it at 5% less and sold it for Rs 160 more, he would have gained 20%. Find the cost price.
  A.  Rs 4000
  B.  Rs 3000
  C.  Rs 5000
  D.  Rs 4200
     
   
View Answer

Shortcut:
A person sells an article at a gain of a%. If he had bought it at b% less and sold it for Rs 'Z' more, he would have gained c%, then the cost price is given by Rs
1002 x Z / 100(c − b − a) − (c x b)

Here, a = 10, b = 5, c = 20, Z = 160
Using these value in shortcut, we get:
Cost Price = Rs
1002 x 160 / 100(20 − 5 − 10) − 20 x 5
= Rs
100 x 100 x 160 / 100 (5) − 100
= Rs
100 x 100 x 160 / 500 − 100
= Rs
100 x 100 x 160 / 400
= 100 x 4 = Rs 400
Hence, cost price will be Rs 4000

32. A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs 55 more he would have had profit of 40%. Find the cost price of the article.
  A.  Rs 220
  B.  Rs 250
  C.  Rs 270
  D.  Rs 240
     
   
View Answer

Shortcut:
A person sells an article at a loss of a%. If he had bought it at b% less and sold it for Rs 'Z' more, he would have gained c%, then the cost price is given by Rs
1002 x Z / 100(c + a − b) − (c x b)

Here, a = 10, b = 20, c = 40, Z = 55
Using these value in shortcut, we get:
Cost Price = Rs
1002 x 55 / 100(40 + 10 − 20) − 40 x 20
= Rs
100 x 100 x 55 / 100 (30) − 800
= Rs
100 x 100 x 55 / 3000 − 800
= Rs
100 x 100 x 55 / 2200
= 50 x 5 = Rs 250
Hence, cost price will be Rs 250

33. A man sells an article at a profit of 20%. If he bought it at 20% less and sold it for Rs 75 less, he would have gained 25%. What is the cost price?
  A.  Rs 335
  B.  Rs 375
  C.  Rs 330
  D.  Rs 320
     
   
View Answer

Shortcut:
A person sells an article at a profit of a%. If he had bought it at b% less and sold it for Rs 'Z' less, he would have gained c%, then the cost price is given by Rs
1002 x Z / 100(a + b − c) + (c x b)

Here, a = 20, b = 20, c = 25, Z = 75
Using these value in shortcut, we get:
Cost Price = Rs
1002 x 75 / 100(20 + 20 − 25) + 25 x 20
= Rs
100 x 100 x 75 / 100 (15) + 500
= Rs
100 x 100 x 75 / 1500 + 500
= Rs
100 x 100 x 75 / 2000
= 5 x 75 = Rs 375
Hence, cost price will be Rs 375

34. A dealer sold a radio at a loss of 2.5%. Had he sold it for Rs 100 more, he would have gained 7.5%. For what value should he sell it in order to gain 12
1 / 2
%? Find the initial cost price also.
  A.  S.P = Rs 1125; C.P = Rs 1000
  B.  S.P = Rs 1225; C.P = Rs 900
  C.  S.P = Rs 1025; C.P = Rs 1100
  D.  S.P = Rs 1155; C.P = Rs 1500
     
   
View Answer

Shortcut:
A person sells an article at a loss of a%. If he had sold it for Rs 'Z' more, he would have gained b%. In order to gain c%, the selling price and the cost price of the article are given by Rs
Z(100 + c) / a + b
and
Zx100 / a + b
respectively.
Here, a = 2.5, b = 7.5, c = 12
1 / 2
or 12.5, Z = 100
Using these value in shortcut, we get:
Selling Price = Rs
100 (100 + 12.5) / 2.5 + 7.5
= Rs
100 (112.5) / 2.5 + 7.5
= Rs
100 x 112.5) / 10
= Rs 1125
Hence, the selling price of the article will be Rs 1125
Cost Price = Rs
100 x 100 / 10
= 1000
Hence, cost price will be Rs 1000

35. A hawker sells organges at a profit of 25%. If he increases the selling price of each orange by 30 paise, he earns a profit of 40%. Find the cost price and the initial selling price of each orange.
  A.  Cost Price: 250 Paise; Initial Selling Price: 200 Paise
  B.  Cost Price: 200 Paise; Initial Selling Price: 250 Paise
  C.  Cost Price: 220 Paise; Initial Selling Price: 260 Paise
  D.  Cost Price: 190 Paise; Initial Selling Price: 210 Paise
     
   
View Answer

Shortcut:
A person sells an article at a profit of a%. If he increases its price by Rs 'Z', he gets gain of b%. The cost price and selling price of the article are given by
Z x 100 / b − a
and Rs
Z(100 + a) / b − a
respectively.
Here, a = 25, b = 40, Z = 30
Using these value in shortcut, we get:
Cost Price = Rs
Z x 100 / b − a
=
30 x 100 / 40 − 25
=
3000 / 15
= 200 Paise
Hence, cost price of oranges be 200 paise
Initial Selling Price = Rs
Z(100 + a) / b − a
=
30 (100 + 25) / 40 − 25
=
30 x 125 / 15
= 2 x 125 = 250 Paise
Hence, initial selling price of oranges be 250 paise.

36. A man had to sell wheat at a loss of 10%. If he increases the price by Rs 5 per kg, he would make a profit of 20%. Find the cost price and initial selling price per kg of wheat.
  A.  Cost Price: Rs 16
2 / 3
per kg; Initial selling price : Rs 15 per kg
  B.  Cost Price: Rs18
3 / 2
per kg; Initial selling price : Rs 16 per kg
  C.  Cost Price: Rs 13
1 / 7
per kg; Initial selling price : Rs 10 per kg
  D.  Cost Price: Rs 17
3 / 5
per kg; Initial selling price : Rs 20 per kg
     
   
View Answer

Shortcut:
A person sells an article at a loss of a%. If he sells it at Rs 'Z' more, he gets gains of b%. Then, the cost price and selling price of the article are given by
Z x 100 / a + b
and Rs
Z(100 − a) / a + b
respectively.
Here, a = 10, b = 20, Z = 5
Using these value in shortcut, we get:
Cost Price = Rs
5 x 100 / 10 + 20
=
500 / 30
=
50 / 3
= 16
2 / 30
per kg
Hence, cost price of wheat be Rs 16
2 / 30
per kg.
Initial Selling Price = Rs
Z(100 − 10) / 10 + 20
=
5 x 90 / 30
= 15 per kg.
Hence, initial selling price of wheat be 15 per kg.

37. A dealer sold a TV at a profit of 20%. Had he sold it for Rs 100 less, he would have gained 15%. For what value should he sell it in order to gain 25%? Also find the initial cost price?
  A.  Selling Price: Rs 2200; Initial cost price: Rs 1800
  B.  Selling Price: Rs 2600; Initial cost price: Rs 2200
  C.  Selling Price: Rs 2300; Initial cost price: Rs 2500
  D.  Selling Price: Rs 2500; Initial cost price: Rs 2000
     
   
View Answer

Shortcut:
A person sells an article at a profit of a%. Had he sold it for Rs 'Z' less, he would have still gained of b%.In order to gain c%, selling price and initial cost price of the article are given by Rs
Z(100 + c) / a − b
and Rs
Z x 100 / a − b
respectively.
Here, a = 20, b = 15, c = 25, Z = 100
Using these value in shortcut, we get:
Selling Price = Rs
Z(100 + c) / a − b
= Rs
100(100 + 25) / 20 − 15
= Rs
100 x 125 / 5
= 100 x 25 = Rs 2500
Hence, selling price of TV be Rs 2500.
Initial Cost Price = Rs
Z x 100 / a − b
= Rs
100 x 100 / 20 − 15
= Rs
100 x 100 / 5
= Rs 2000
Hence, cost price of TV be Rs 2000.

38. A dealer sold a TV at a profit of 15%. Had he sold it for Rs 100 more, he would have gained 20%. For what value should he sell it in orer to gain 25% ? Also find the initial cost price.
  A.  Selling Price: Rs 2600; Initial cost price: Rs 1900
  B.  Selling Price: Rs 2400; Initial cost price: Rs 2300
  C.  Selling Price: Rs 2500; Initial cost price: Rs 2000
  D.  Selling Price: Rs 2000; Initial cost price: Rs 2600
     
   
View Answer

Shortcut:
A person sells an article at a profit of a%. Had he sold it for Rs 'Z' more, he would have gained of b%. In order to gain c%, selling price and initial cost price of the article are given by Rs
Z(100 + c) / b − a
and Rs
Z x 100 / b − a
respectively.
Here, a = 15, b = 20, c = 25, Z = 100
Using these value in shortcut, we get:
Selling Price = Rs
Z(100 + 25) / b − a
= Rs
100(100 + 25) / 20 − 15
= Rs
100 x 125 / 5
= 100 x 25 = Rs 2500
Hence, selling price of radio be Rs 2500.
Initial Cost Price = Rs
Z x 100 / b − a
= Rs
100 x 100 / 20 − 15
= Rs
100 x 100 / 5
= Rs 2000
Hence, cost price of TV be Rs 2000.

39. A dealer sold a TV at a loss of 20%. Had he sold it for Rs 100 more, he would have lost 15%. For what value should he sell it in order to gain 25% . Also find hte initial cost price.
  A.  Selling price: Rs 2800; Initial cost price: Rs 2800
  B.  Selling price: Rs 2500; Initial cost price: Rs 2000
  C.  Selling price: Rs 2100; Initial cost price: Rs 1900
  D.  Selling price: Rs 2600; Initial cost price: Rs 2050
     
   
View Answer

Shortcut:
A person sells an article at a loss of a%. Had he sold it for Rs 'Z' more, he would have still lost of b%. In order to gain c%, selling price and initial cost price of the article are given by Rs
Z(100 + c) / a − b
and Rs
Z x 100 / a − b
respectively.
Here, a = 20, b = 15, c = 25, Z = 100
Using these value in shortcut, we get:
Selling Price = Rs
Z(100 + 25) / a − b
= Rs
100(100 + 25) / 20 − 15
= Rs
100 x 125 / 5
= 100 x 25 = Rs 2500
Hence, selling price of TV be Rs 2500.
Initial Cost Price = Rs
Z x 100 / a − b
= Rs
100 x 100 / 20 − 15
= Rs
100 x 100 / 5
= Rs 2000
Hence, cost price of TV be Rs 2000.

40. An article is sold at a profit of 20%. If both the cost price and selling price are Rs 100 less, the profit would be 4% more. Find the cost price.
  A.  Rs 600
  B.  Rs 580
  C.  Rs 630
  D.  Rs 675
     
   
View Answer

Shortcut:
If an article is sold at a profit of a%. If both the cost price and selling price are Rs Z less, the profit would be b% more, then the cost price is Rs
Z(a + b) / b
.
Here, a = 20, b = 4, Z = 100
Using these value in shortcut, we get:
Cost Price = Rs
100(20 + 4) / 4
= Rs
(100 x 24) / 4
= 100 x 6 = Rs 600
Hence, cost price of article be Rs 600.

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