226. A merchant marks his goods 40% above the cost price and sells them at a discount of 15%. Find his gain %.

1. 1. 25%

   
   
   

   2. 22%

   
   
   

   3. 19%

   
   
   

   4. 20%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the C.P. of each article be ₹ 100.
   ∴  Marked price = ₹ 140
   

   ∴  S.P. =	140 × 85	= ₹ 119
   	100

   
   ∴  Gain percent = 19%
   2nd method to solve this question.
   Here, r = 40%, r₁ = 15%
   

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

   
   

   Correct Option: D

   Let the C.P. of each article be ₹ 100.
   ∴  Marked price = ₹ 140
   

   ∴  S.P. =	140 × 85	= ₹ 119
   	100

   
   ∴  Gain percent = 19%
   2nd method to solve this question.
   Here, r = 40%, r₁ = 15%
   

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

   
   

   Gain % =	40 × (100 − 15)	− 15
   	100

   
   

   Gain % =	40 × 85	− 15
   	100

   
   

   Gain % =	3400	− 15
   	100

   
   Required Gain % = 19%
   

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227. A trader marks his goods at 20% above the cost price. If he allows a discount of 5% for cash down payment, his profit percent for such a transaction is

1. 1. 15%

   
   
   

   2. 12%

   
   
   

   3. 14%

   
   
   

   4. 17%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let C.P. be ₹ 100.
   Marked price = ₹ 120
   

   S.P. =	120 × 95	= ₹ 114
   	100

   
   Gain percent = 14%
   2nd method to solve this question.
   Here, r = 20%, r₁ = 5%
   

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

   
   

   Correct Option: C

   Let C.P. be ₹ 100.
   Marked price = ₹ 120
   

   S.P. =	120 × 95	= ₹ 114
   	100

   
   Gain percent = 14%
   2nd method to solve this question.
   Here, r = 20%, r₁ = 5%
   

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

   
   

   Gain % =	20 × (100 − 5)	− 5
   	100

   
   Required Gain % = 19 – 5 = 14%

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228. If $ 10 be allowed as true discount on a bill of $ 110 due at the end of certain time, then the discount allowed on the same amount due at the end of double the time is :

1. 1. $ 20

   
   
   

   2. $ 21.81

   
   
   

   3. $ 22

   
   
   

   4. $ 18.33

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given :- Amount = $ 110
   S.I. on $ (110 - 10) for a given time = $ 10
   S.I. on $ 100 for double the time = $ 20
   Sum = $ (100 + 20) = $ 120
   

   ∴ True discount =	Amount x Rate x Time
   	100 + Rate x Time

   Correct Option: D

   Given :- Amount = $ 110
   S.I. on $ (110 - 10) for a given time = $ 10
   S.I. on $ 100 for double the time = $ 20
   Sum = $ (100 + 20) = $ 120
   

   ∴ True discount =	Amount x Rate x Time
   	100 + Rate x Time

   
   

   T.D. on $ 110 = $		20	x 110			= $ 18.33
   		120

   
   

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229. The holder of a bill for ₹17850 nominally due on May 21, 1991 received ₹357 less than the amount of the bill by having it discounted at 5 %. When was it discounted?

1. 1. Dec 29, 1990

   
   
   

   2. Dec 30, 1989

   
   
   

   3. Dec 19, 1990

   
   
   

   4. Dec 20, 1995

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , Amount = ₹17850 , Rate = 5% ,
   S.I. on ₹17850 at 5% is ₹357.
   

   ∴ Time =	S.I. x 100
   	Amount x Rate

   
   

   Time =		100 × 357		=	2	Year = 146 Days
   		17850 × 5			5

   
   So, the bill is 146 days prior to May 24, the legally due date.
   Sum of the number of Days ( May + April + March + Feb. + Jan. + Dec. ) = 24 + 30 + 31 + 28 + 31 + 2 = 146 days So, the bill was discounted on Dec 29, 1990.

   Correct Option: A

   Here , Amount = ₹17850 , Rate = 5% ,
   S.I. on ₹17850 at 5% is ₹357.
   

   ∴ Time =	S.I. x 100
   	Amount x Rate

   
   

   Time =		100 × 357		=	2	Year = 146 Days
   		17850 × 5			5

   
   So, the bill is 146 days prior to May 24, the legally due date.
   Sum of the number of Days ( May + April + March + Feb. + Jan. + Dec. ) = 24 + 30 + 31 + 28 + 31 + 2 = 146 days So, the bill was discounted on Dec 29, 1990.

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230. At a given rate, the simple interest and the true discount on a certain sum, for a given time, are ₹24 and ₹22, respectively. The sum is :

1. 1. ₹264

   
   
   

   2. ₹220

   
   
   

   3. ₹288

   
   
   

   4. ₹295

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given :- True discount = ₹ 24 and Simple Interest = ₹ 22
   

   ∴ Sum Due =	True discount × Simple Interest
   	Simple Interest - True discount

   Correct Option: A

   Given :- True discount = ₹ 24 and Simple Interest = ₹ 22
   

   ∴ Sum Due =	True discount × Simple Interest	=	24 × 22	= ₹ 264
   	Simple Interest - True discount		24 - 22

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