6. Two shopkeepers announce the same price of Rs. 700 for a sewing machine. The first offers successive discounts of 30% and 6% while the second offers successive discounts of 20% and 16%. The difference in their selling price is :

1. 1. Rs. 9.8

   
   
   

   2. Rs. 16.8

   
   
   

   3. Rs. 22.4

   
   
   

   4. Rs. 36.4

   
   
   

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1. View Hint View Answer Discuss in Forum

   For the first shopkeeper,
   Single equivalent discount for two successive discounts of 30% and 6%
   

   =		30 + 6 −	30 × 6		%
   			100

   
   = ( 36 –1.8 ) % = 34.2 %
   ∴  S.P. of sewing machine = ( 100 – 34.2 ) % of Rs. 700
   
   For the second shopkeeper,
   Single equivalent discount
   

   =		20 + 16 −	20 × 16		%
   			100

   
   = ( 36 – 3.2 )% = 32.8 %
   ∴  S.P. of sewing machine = 700 × ( 100 – 32.8 ) %

   Correct Option: A

   For the first shopkeeper,
   Single equivalent discount for two successive discounts of 30% and 6%
   

   =		30 + 6 −	30 × 6		%
   			100

   
   = ( 36 –1.8 ) % = 34.2 %
   ∴  S.P. of sewing machine = ( 100 – 34.2 ) % of Rs. 700
   

   = Rs.		700 × 65.8		= Rs. 460.6
   		100

   
   For the second shopkeeper,
   Single equivalent discount
   

   =		20 + 16 −	20 × 16		%
   			100

   
   = ( 36 – 3.2 )% = 32.8 %
   ∴  S.P. of sewing machine = 700 × ( 100 – 32.8 ) %
   

   = Rs.		700 × 67.8		= Rs. 470.4
   		100

   
   Required difference = Rs. (470.4 – 460.6) = Rs. 9.8
   Alternate method to find the difference
   Difference between single equivalent discounts = ( 34.2 – 32.8 ) % = 1.4 %
   

   ∴  Difference of S.P. = Rs.		700 × 1.4		= Rs. 9.8
   		100

   
   

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7. When a discount of 20% is given on a sweater, the profit is 28%. If the discount is 14%, then the profit is

1. 1. 42 percent

   
   
   

   2. 46.4 percent

   
   
   

   3. 33.2 percent

   
   
   

   4. 37.6 percent

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the C.P. of sweater be Rs. 100 and its marked price be Rs. x.
   According to the question,
   

   x ×	80	= 128
   	100

   
   

   ⇒  x ×	4	= 128
   	5

   Correct Option: D

   Let the C.P. of sweater be Rs. 100 and its marked price be Rs. x.
   According to the question,
   

   x ×	80	= 128
   	100

   
   

   ⇒  x ×	4	= 128
   	5

   
   

   ⇒  x =	128 × 5	= Rs. 160
   	4

   
   When discount = 14%, then
   S.P. of sweater
   = 160 × (100 – 1(4)%
   

   =	160 × 86	= Rs. 137.6
   	100

   
   ∵  C.P. = Rs. 100
   ∴  Profit per cent = 37.6%
   

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8. 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%

   
   
   

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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
   

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9. 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%

   
   
   

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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%

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10. Anand marks up the price of an article by 50 % and then allows a discount of 20 % and sells it to Balaji. Balaji sells it for ₹ 20 more than what he purchased for, this S.P is 30 % more than the original C.P of the article. Then Balaji’s profit % is

1. 1. 7.5%

   
   
   

   2. 6.66%

   
   
   

   3. 8.33%

   
   
   

   4. 9%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let us assume the cost price = ₹ p
   For Anand,
   

   Marked price = ₹	3	p
   	2

   
   

   Selling price =	3p	×	80
   	2		100

   
   For Balaji,
   

   Cost price = ₹	6p
   	5

   
   

   Selling price = ₹		6p	+ 20
   		5

   
   

   ∴	6p	+ 20 =	p × 130
   	5		100

   
   

   Correct Option: C

   Let us assume the cost price = ₹ p
   For Anand,
   

   Marked price = ₹	3	p
   	2

   
   

   Selling price =	3p	×	80
   	2		100

   
   

   = ₹	6p
   	5

   
   For Balaji,
   

   Cost price = ₹	6p
   	5

   
   

   Selling price = ₹		6p	+ 20
   		5

   
   

   ∴	6p	+ 20 =	p × 130
   	5		100

   
   

   ⇒	13p	−	6p	= 20
   	10		5

   
   

   ⇒	13p − 12p	= 20
   	10

   
   

   ⇒	p	= 20
   	10

   
   ⇒  p = ₹ 200
   

   ∴  Required gain percent =	20	×100
   	6p
   	5

   
   

   ⇒  Required gain percent =	20 × 5 × 100
   	6 × p

   
   

   ⇒  Required gain percent =	20 × 5 × 100	=	25	= 8.33%
   	6 × 200		3

   
   ∴ Required gain percent is 8.33% .

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