41. A dealer marks his goods 20% above their cost price. He then allows some discount on marked price so that he makes a profit of 10%. The rate of discount is

1. 1. 10	1	%
      	3

   
   
   

   2. 9	1	%
      	3

   
   
   

   3. 8	2	%
      	3

   
   
   

   4. 8	1	%
      	3

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let cost price of article = ₹ 100
   

   ∴  Marked price of article =	100 × 120	= ₹ 120
   	100

   
   S.P. of article = ₹ 110
   ∴  Discount = 120 – 110 = ₹ 10
   ∴  Let us assume that the discount = p %, then solve the question.
   2nd method to solve this question.
   Here, r = 20%, Profit = 10%
   Let, discount r₁ = p%
   

   Profit % =	r ×(100 − r1)	− r1
   	100

   
   

   Correct Option: D

   Let cost price of article = ₹ 100
   

   ∴  Marked price of article =	100 × 120	= ₹ 120
   	100

   
   S.P. of article = ₹ 110
   ∴  Discount = 120 – 110 = ₹ 10
   ∴  Let us assume that discount = p %, then
   

   12 × p	= 10
   100

   
   
   

   ⇒  p=	10 × 100	=	25	= 8	1	%
   	120		3		3

   
   2nd method to solve this question.
   Here, r = 20%, Profit = 10%
   Let, discount r₁ = p%
   

   Profit % =	r ×(100 − r1)	− r1
   	100

   
   

   10 =	20 × (100 − p)	− r1
   	100

   
   1000 = 2000 – 20p – 100p
   –1000 = –120p
   

   p =	100
   	12

   
   

   p =	25	= 8	1	%
   	3		3

---

42. A shopkeeper marks the price of an item keeping 20% profit. If he offers a discount of

    12	1	% on the marked price, his gain percent will be
    	2

1. 1. 4.5%

   
   
   

   2. 5%

   
   
   

   3. 7.5%

   
   
   

   4. 8%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the cost price be ₹ 100.
   ∴  Marked price = ₹ 120
   

   SP = 87	1	% of 120
   	2

   
   

   =	175	× 120 = ₹ 105
   	200

   
   ∴  Gain percent = 5%
   Gain percent = 5%
   2nd method to solve this question.
   Here, r = 20%,
   

   r1 = 12	1	%
   	2

   
   

   Correct Option: B

   Let the cost price be ₹ 100.
   ∴  Marked price = ₹ 120
   

   SP = 87	1	% of 120
   	2

   
   

   =	175	× 120 = ₹ 105
   	200

   
   ∴  Gain percent = 5%
   Gain percent = 5%
   2nd method to solve this question.
   Here, r = 20%,
   

   r1 = 12	1	%
   	2

   
   

   Profit % =	r × (100 − r1)	− r1
   	100

   
   
   
   

   Profit % =	20 ×		100 −	25		−
   				2			25
   			100				2

   
   

   Profit % =	20 × 175	− 12.5
   	200

   
   Required Profit % = 17.5 – 12.5 = 5%
   

---

---

43. A shopkeeper marks his goods at 30% above the cost price but allows a discount of 10% at the time of sale. His gain is

1. 1. 21%

   
   
   

   2. 20%

   
   
   

   3. 18%

   
   
   

   4. 17%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let the CP of the article be 100.
   According to the question,
   The marked price = ₹ 130
   Discount = 10%
   

   ∴  SP = 90% of 130 =	130 × 90	= ₹ 117
   	100

   
   ∴  Gain = 117 – 100 = ₹ 17
   ∴  Gain percent = 17% since the CP = ₹ 100
   2nd method to solve this question.
   Here, r = 30%, r₁ = 10%
   

   gain % =	r × (100 − r1)	− r1
   	100

   
   

   Correct Option: D

   Let the CP of the article be 100.
   According to the question,
   The marked price = ₹ 130
   Discount = 10%
   

   ∴  SP = 90% of 130 =	130 × 90	= ₹ 117
   	100

   
   ∴  Gain = 117 – 100 = ₹ 17
   ∴  Gain percent = 17% since the CP = ₹ 100
   2nd method to solve this question.
   Here, r = 30%, r₁ = 10%
   

   gain % =	r × (100 − r1)	− r1
   	100

   
   

   gain % =	30 × (100 − 10)	− 10
   	100

   
   

   gain % =	30 × 90	− 10 = 17 %
   	100

   
   

---

44. A trader marked the selling price of an article at 10% above the cost price. At the time of selling, he allows certain discount and suffers a loss of 1%. He allowed the discount of :

1. 1. 11%

   
   
   

   2. 10%

   
   
   

   3. 9%

   
   
   

   4. 10.5%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Let C.P. be 100
   Marked price = 110
   ∴  p% of 110 = 11
   

   ⇒  p =	11 × 100	= 10%
   	100

   
   2nd method to solve this question.
   Here, loss % = 1%, r = 10%, r₁ = p%
   

   loss % =	r × (100 − r1)	− r1
   	100

   
   

   −1 =	100 × (100 − p)	− p
   	100

   
   

   Correct Option: B

   Let C.P. be 100
   Marked price = 110
   ∴  p% of 110 = 11
   

   ⇒  p =	11 × 100	= 10%
   	100

   
   2nd method to solve this question.
   Here, loss % = 1%, r = 10%, rr₁ = p%
   

   loss % =	r × (100 − r1)	− r1
   	100

   
   

   −1 =	100 × (100 − p)	− p
   	100

   
   (–ve sign for loss)
   –100 = 1000 – 10p – 100p
   110p = 1100
   p = 10%
   ⇒  r₁ = 10%

---

---

45. A tradesman marks his goods at 20% above the cost price. He allows his customers a discount of 8% on marked price. Find out his profit %.

1. 1. 12%

   
   
   

   2. 10.4%

   
   
   

   3. 8.6%

   
   
   

   4. 8.2%

   
   
   

---

1. View Hint View Answer Discuss in Forum

   Suppose C.P. = 100
   On 20% above S.P. = 120
   

   On discount of 8% = 120 − 120 ×	8
   	100

   
   

   New S.P. = 120 −	48	= 120 − 9.6 = 110.4
   	5

   
   Gain = 110.4 – 100 = 10.4%
   2nd method to solve this question
   Here, r = 20%, r₁ = 8%
   

   Profit or loss =	r ×(100 − r1)	−r1
   	100

   
   

   Profit or loss =	20 ×(100 − 8)	− 8
   	100

   
   

   Correct Option: B

   Suppose C.P. = 100
   On 20% above S.P. = 120
   

   On discount of 8% = 120 − 120 ×	8
   	100

   
   

   New S.P. = 120 −	48	= 120 − 9.6 = 110.4
   	5

   
   Gain = 110.4 – 100 = 10.4%
   2nd method to solve this question
   Here, r = 20%, r₁ = 8%
   

   Profit or loss =	r ×(100 − r1)	−r1
   	100

   
   

   Profit or loss =	20 ×(100 − 8)	− 8
   	100

   
   

   Profit or loss =	20 × 92	− 8
   	100

   
   = 18.4 – 8
   Required Profit or loss = 10.4% profit
   

---