231. A man bought a motor-cycle for ₹32500. He sold it for ₹35000, allowing the buyer for a 6 months credit. If the money be worth 4 % per annum, the gain percent is :

1. 1. 8	1	%
      	7

   
   
   

   2. 7	9	%
      	13

   
   
   

   3. 7	5	%
      	13

   
   
   

   4. 8	2	%
      	5

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , Selling Price of motor- cycle = ₹35000
   Cost Price of motor- cycle = ₹32500
   ∴ Gain = Selling Price - Cost Price
   Gain = ₹35000 - ₹32500
   Gain = ₹2500
   

   ∴ Gain % =	Gain	× 100 %
   	Cost Price

   Correct Option: B

   Here , Selling Price of motor- cycle = ₹35000
   Cost Price of motor- cycle = ₹32500
   ∴ Gain = Selling Price - Cost Price
   Gain = ₹35000 - ₹32500
   Gain = ₹2500
   

   ∴ Gain % =	Gain	× 100 %
   	Cost Price

   
   

   ∴ Gain % =	2500	× 100 %
   	32500

   =	100	% = 7	9	%
   	13		7

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232. A banker discounts a 4 months bill at 3 %. If the proceeds be invested in a manner, so that nothing is lost, the interest rate should be :

1. 1. 3%

   
   
   

   2. 4%

   
   
   

   3. 3	1	%
      	33

   
   
   

   4. 3	1	%
      	36

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , 4 months =	1	years
   	3

   & there4; Banker deducts ₹3 ×	1	= ₹1 from a bill of ₹100
   	3

   
   Banker 's discount = ₹1
   So, the banker pays ₹(100 - 1) = ₹99.
   Amount = ₹ 99
   So, the bill-holder loses ₹1.
   So, for investment ₹1 should be interest on ₹99 for 4 months.
   

   ∴ Rate of interest =	Banker 's discount × 100	%
   	Amount × Time

   
   

   ∴ Rate of interest =	1 × 100	=	100	= 3	1	%
   	99 × 4/12		33		33

   Correct Option: C

   Here , 4 months =	1	years
   	3

   & there4; Banker deducts ₹3 ×	1	= ₹1 from a bill of ₹100
   	3

   
   Banker 's discount = ₹1
   So, the banker pays ₹(100 - 1) = ₹99.
   Amount = ₹ 99
   So, the bill-holder loses ₹1.
   So, for investment ₹1 should be interest on ₹99 for 4 months.
   

   ∴ Rate of interest =	Banker 's discount × 100	%
   	Amount × Time

   
   

   ∴ Rate of interest =	1 × 100	=	100	= 3	1	%
   	99 × 4/12		33		33

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233. The present worth of a sum of money due for 146 days at 5 % is ₹400. The sum due is :

1. 1. ₹410

   
   
   

   2. ₹408

   
   
   

   3. ₹415

   
   
   

   4. ₹450

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given :- Present worth = ₹400 , Rate = 5%

   Time = 146 days =	146	years
   	365

   
   

   True Discount =	P.W. × Time × Rate
   	100

   
   

   Correct Option: B

   Given :- Present worth = ₹400 , Rate = 5%

   Time = 146 days =	146	years
   	365

   
   

   True Discount =	P.W. × Time × Rate
   	100

   
   

   True Discount = ₹400 ×	146	×	5	= ₹8
   	365		100

   
   Sum due = Present worth + True Discount
   Sum due = ₹400 + ₹8 = ₹408.

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234. The present worth of a bill of ₹1764 due for 2 years at 5 % compound interest is :

1. 1. ₹1650

   
   
   

   2. ₹1700

   
   
   

   3. ₹1600

   
   
   

   4. ₹1714

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that :- Amount = ₹1764 , Rate = 5% and Time = 2 years
   

   ∴ Present Worth ( P.W. ) = Amount ÷		1 +	Rate		Time
   			100

   
   

   Correct Option: C

   Given that :- Amount = ₹1764 , Rate = 5% and Time = 2 years
   

   ∴ Present Worth ( P.W. ) = Amount ÷		1 +	Rate		Time
   			100

   
   

   P.W. = ₹1764 ÷		1 +	5		×		1 +	5
   			100					100

   = ₹1764 ×	440	= ₹1600
   	441

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235. The banker’s gain on a certain sum of money is due for 9 months at 4 % p.a. is ₹2.25. The sum is :

1. 1. ₹2575

   
   
   

   2. ₹2500

   
   
   

   3. ₹2250

   
   
   

   4. ₹3250

   
   
   

   5. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , Banker 's Gain = ₹2.25 , Time = 9 months =	9	=	3	years
   	12		4

   
   Banker 's Gain is the interest on True Discount .
   

   True discunt =	Banker 's Gain × 100
   	Rate × Time

   ∴ True Discount ( T.D. ) =	2.25 × 100	= ₹ 75
   	3/4 × 4

   
   Banker 's Discount ( B.D. ) = True Discount ( T.D. ) + Banker 's Gain ( B.G. )
   B.D.= ₹75 + ₹2.25 = ₹77.25
   

   ∴ Sum due =	B.D. × T.D.
   	B.G.

   
   

   Correct Option: A

   Here , Banker 's Gain = ₹2.25 , Time = 9 months =	9	=	3	years
   	12		4

   
   Banker 's Gain is the interest on True Discount .
   

   True discunt =	Banker 's Gain × 100
   	Rate × Time

   ∴ True Discount ( T.D. ) =	2.25 × 100	= ₹ 75
   	3/4 × 4

   
   Banker 's Discount ( B.D. ) = True Discount ( T.D. ) + Banker 's Gain ( B.G. )
   B.D.= ₹75 + ₹2.25 = ₹77.25
   

   ∴ Sum due =	B.D. × T.D.	= ₹	77.25 × 75
   	B.G.		2.25

   
   Sum due = ₹ 2575.

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