16. At some rate of simple interest, A lent 6,000 to B for 2 years and 1,500 to C for 4 years and received 9,00 as interest from both of them together. The rate of interest per annum was
    

1. 1. 5%
      

   
   
   

   2. 6%
      

   
   
   

   3. 8%
      

   
   
   

   4. 10%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , P₁ = ₹ 6000 , P₂ = ₹ 1500 , T₁ = 2 years , T₂ = 4 years and SI = ₹ 900
   If rate of interest be R% per annum then,
   

   SI =	Principal × Time × Rate
   	100

   
   

   Correct Option: A

   Here , P₁ = ₹ 6000 , P₂ = ₹ 1500 , T₁ = 2 years , T₂ = 4 years and SI = ₹ 900
   If rate of interest be R% per annum then,
   

   SI =	Principal × Time × Rate
   	100

   
   

   ∴ 900 =	6000 × 2 × R	+	1500 × 4 × R
   	100		100

   
   ⇒ 120R + 60R = 900
   ⇒ 180R = 900
   ⇒ R = 900 ÷ 180 = 5%

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17. What sum of money must be given as simple interest for six months at 4% per annum in order to earn 150 interest?
    

1. 1. 5000
      

   
   
   

   2. 7500
      

   
   
   

   3. 10000
      

   
   
   

   4. 15000

   
   
   

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1. View Hint View Answer Discuss in Forum

   As we know that ,
   

   P =	Simple interest × 100
   	Rate × Time

   
   

   Correct Option: B

   As we know that ,
   

   P =	Simple interest × 100
   	Rate × Time

   
   

   P =	150 × 100	×	2	= ₹ 7500
   	4		1

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18. A sum of money becomes 41/40 of itself in 1/4 years at a certain rate of simple interest. The rate of interest per annum is
    

1. 1. 10%
      

   
   
   

   2. 1%
      

   
   
   

   3. 2.5%
      

   
   
   

   4. 5%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the principal be Re.1
   ∴ SI = Amount - Principle
   

   S.I. =	41	- 1 =	1
   	40		40

   
   

   Now, rate =	Interest × 100
   	Principal × Time

   
   

   Rate =	(1 ÷ 40) × 100	=	100 × 4	= 10%
   	1 × (1 ÷ 4)		40

   
   Second method to solve this question :
   

   R =		41	- 1		× 100
   		40
   		1
   		4

   
   

   Correct Option: A

   Let the principal be Re.1
   ∴ SI = Amount - Principle
   

   S.I. =	41	- 1 =	1
   	40		40

   
   

   Now, rate =	Interest × 100
   	Principal × Time

   
   

   Rate =	(1 ÷ 40) × 100	=	100 × 4	= 10%
   	1 × (1 ÷ 4)		40

   
   Second method to solve this question :
   

   R =		41	- 1		× 100
   		40
   		1
   		4

   
   

   R =	1	× 4 × 100%
   	40

   
   R = 10%

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19. The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10,000, the present population is
    

1. 1. 4600
      

   
   
   

   2. 6400
      

   
   
   

   3. 7600
      

   
   
   

   4. 6000

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , R = 20% , 2 years ago population = 10,000
   We can find the required answer with the help of given formula ,
   

   Present population = 10000		1 -	R		2
   			100

   
   

   Present population = 10000		1 -	20		2
   			100

   
   

   Correct Option: B

   Here , R = 20% , 2 years ago population = 10,000
   We can find the required answer with the help of given formula ,
   

   Present population = 10000		1 -	R		2
   			100

   
   

   Present population = 10000		1 -	20		2
   			100

   
   

   Present population = 10000 ×	4	×	4	= 6400
   	5		5

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20. The sum lent at 5% per annum (i.e. 365 days) simple interest, that produces interest, of ₹2.00 a day, is
    

1. 1. ₹1,400
      

   
   
   

   2. ₹14,700
      

   
   
   

   3. ₹14,600
      

   
   
   

   4. ₹7,300

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question ,
   Annual interest = 365 × 2 = 730
   We know that ,
   

   Principal =	SI × 100
   	Time × Rate

   
   

   Correct Option: C

   According to question ,
   Annual interest = 365 × 2 = 730
   We know that ,
   

   Principal =	SI × 100
   	Time × Rate

   
   

   Principal =	730 × 100
   	1 × 5

   
   Principal = 14600

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