76. A person sold an article at 20% profit on the selling price. Afterwards, when the cost price reduced by 10%, then he also reduced the selling price by 10%. His percentage of profit on cost price will be

1. 1. 30%

   
   
   

   2. 25%

   
   
   

   3. 22.5%

   
   
   

   4. 12.5%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , Gain % = 20%
   

   Gain percent =	Gain	× 100
   	S.P.

   
   

   ⇒ 20 =	S.P. - C.P.	× 100
   	S.P.

   
   ⇒ S.P. = 5 (S.P. – C.P.)
   ⇒ 5 C.P. = 5 S.P. – S.P. = 4 S.P.
   

   Correct Option: B

   Here , Gain % = 20%
   

   Gain percent =	Gain	× 100
   	S.P.

   
   

   ⇒ 20 =	S.P. - C.P.	× 100
   	S.P.

   
   ⇒ S.P. = 5 (S.P. – C.P.)
   ⇒ 5 C.P. = 5 S.P. – S.P. = 4 S.P.
   

   ⇒ S.P. =	5	C.P. =		1 +	1			C.P.
   	4				4

   
   ∴ Required gain percent = 25%

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77. A cloth merchant sold half of his cloth at 40% profit, half of remaining at 40% loss and the rest was sold at the cost price. In the total transaction his gain or loss will be

1. 1. 20% gain

   
   
   

   2. 25% loss

   
   
   

   3. 10% gain

   
   
   

   4. 15% loss

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the merchant bought 100 metres of cloth for $ 100.
   From question ,
   

   ∴ Total S.P = $		50 × 140	+	25 × 60	+ 25
   		100		100

   
   

   Correct Option: C

   Let the merchant bought 100 metres of cloth for $ 100.
   From question ,
   

   ∴ Total S.P = $		50 × 140	+	25 × 60	+ 25
   		100		100

   
   Total S.P = (70 + 15 + 25) = $ 110
   Gain = 110 - 100 = $ 10
   

   ∴ Gain % =	10	× 100 = 10%
   	100

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78. The percentage of profit, when an article is sold for $ 78, is twice than when it is sold for $ 69. The cost price of the article is :

1. 1. $ 49

   
   
   

   2. $ 51

   
   
   

   3. $ 57

   
   
   

   4. $ 60

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the C.P. of article be y.
   Then, According to question,
   

   			78 - y		× 100	=	2 ×		69 - y		× 100
   			y						y

   
   

   Correct Option: D

   Let the C.P. of article be y.
   Then, According to question,
   

   			78 - y		× 100	=	2 ×		69 - y		× 100
   			y						y

   
   ⇒ 78 – y = 2 × 69 – 2y
   ⇒ 2y – y = 138 – 78
   ⇒ y = $ 60

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79. If the total cost of 73 articles having equal cost is $ 5,110 and the total selling price of 89 such articles is $ 5,607, then in the transaction, there will be

1. 1. a loss of 15%

   
   
   

   2. a gain of 10%

   
   
   

   3. a loss of 10%

   
   
   

   4. a gain of 15%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given in question , CP of 73 articles = $ 5110
   

   ∴ CP of 89 articles =	5110	× 89 = 6230
   	73

   
   Total SP of 89 articles = $ 5607
   Loss = $ (6230 – 5607) = $ 623
   

   ∴ Loss percent =	Loss	× 100
   	CP of 89 articles

   
   

   Correct Option: C

   Given in question , CP of 73 articles = $ 5110
   

   ∴ CP of 89 articles =	5110	× 89 = 6230
   	73

   
   Total SP of 89 articles = $ 5607
   Loss = $ (6230 – 5607) = $ 623
   

   ∴ Loss percent =	Loss	× 100
   	CP of 89 articles

   
   

   Loss percent =	623	× 100 = 10%
   	6230

   
   

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80. By selling 60 articles a vendor gains the selling price of 15 articles. Find his gain percentage.

1. 1. 25 %

   
   
   

   2. 33	1	%
      	3

   
   
   

   3. 20%

   
   
   

   4. 28	4	%
      	7

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the S.P. of 60 articles be y.
   

   ∴ S.P. of 15 articles =	y
   	4

   
   

   C.P. of 60 articles = y -		y	=	3y
   		4		4

   
   

   Gain = y -		3y	=	y
   		4		4

   
   

   ∴ Gain % =	( y / 4)	× 100
   	( 3y / 4 )

   
   

   Gain % =		y	×	4	× 100
   		4		3y

   
   

   Gain% =		100	= 33	1	%
   		3		3

   
   We can find required answer with the help of given formula :
   Here, p = 60, q = 15
   

   Gain% =	q × 100
   	p - q

   
   

   Correct Option: B

   Let the S.P. of 60 articles be y.
   

   ∴ S.P. of 15 articles =	y
   	4

   
   

   C.P. of 60 articles = y -		y	=	3y
   		4		4

   
   

   Gain = y -		3y	=	y
   		4		4

   
   

   ∴ Gain % =	( y / 4)	× 100
   	( 3y / 4 )

   
   

   Gain % =		y	×	4	× 100
   		4		3y

   
   

   Gain% =		100	= 33	1	%
   		3		3

   
   We can find required answer with the help of given formula :
   Here, p = 60, q = 15
   

   Gain% =	q × 100
   	p - q

   
   

   Gain% =	15 × 100
   	60 - 15

   
   

   Gain% =	15 × 100
   	45

   
   

   Gain% =		100	= 33	1	%
   		3		3

   
   

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