11. 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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12. 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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13. What sum of money will amount to 520 in 5 years and to 568 in 7 years at simple interest ?
    

1. 1. 400
      

   
   
   

   2. 120
      

   
   
   

   3. 510
      

   
   
   

   4. 220

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that , A₁ = ₹ 520 , A₂ = ₹ 568 , T₁ = 5 years , T₂ = 7 years
   Simple interest for 2 years = ₹(568 – 520) = ₹ 48
   

   ∴ Interest for 5 years = ₹	48	× 5 = ₹ 120
   	2

   
   Principal = Amount - Simple Interest = (520 – 120) = 400
   Second method to solve this question :
   Here , A₂ = ₹ 568 , T₁ = 5 years , A₁ = ₹ 520 , T₂ = 7 years
   

   P =		A2T1 - A1T2
   		T12

   
   

   P =		568 × 5 - 520 × 7
   		5 - 7

   
   

   Correct Option: A

   Given that , A₁ = ₹ 520 , A₂ = ₹ 568 , T₁ = 5 years , T₂ = 7 years
   Simple interest for 2 years = ₹(568 – 520) = ₹ 48
   

   ∴ Interest for 5 years = ₹	48	× 5 = ₹ 120
   	2

   
   Principal = Amount - Simple Interest = (520 – 120) = 400
   Second method to solve this question :
   Here , A₂ = ₹ 568 , T₁ = 5 years , A₁ = ₹ 520 , T₂ = 7 years
   

   P =		A2T1 - A1T2
   		T12

   
   

   P =		568 × 5 - 520 × 7
   		5 - 7

   
   

   P =		2840 - 3640
   		- 2

   
   P = (- 800 ) ÷ ( -2 ) = ₹ 400

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14. A certain sum of money amounts to 756 in 2 years and to 873 in 3	1
    	3

    years at a certain rate of simple interest. The rate of interest per annum is
    

1. 1. 10%
      

   
   
   

   2. 11%
      

   
   
   

   3. 12%
      

   
   
   

   4. 13%

   
   
   

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1. View Hint View Answer Discuss in Forum

   SI for 1	1	yrs = ₹(873 – 756) = ₹117
   	2

   
   

   S.I. for 2 years = ₹		117 ×	2	× 2		= ₹156
   			3

   
   ∴ Principal = 756 – 156 = ₹600
   Now, P = ₹ 600, T = 2 years , S.I. = ₹ 156
   

   ∴ R =	100 × S.I
   	P × T

   
   

   R =	100 × 156	= 13%
   	600 × 2

   
   Second method to solve this question :
   Here , A₂ = ₹ 873 , T₁ = 2 years , A₁ = ₹ 756 , T₂ = 3.5 years = 7 / 2 years
   

   Rate of interest =		A1 - A2		× 100
   		A2T1 - A1T2

   
   

   Rate of interest =		756 -873			× 100
   		873 ×2 - 756 ×	7
   			2

   
   

   Correct Option: D

   SI for 1	1	yrs = ₹(873 – 756) = ₹117
   	2

   
   

   S.I. for 2 years = ₹		117 ×	2	× 2		= ₹156
   			3

   
   ∴ Principal = 756 – 156 = ₹600
   Now, P = ₹ 600, T = 2 years , S.I. = ₹ 156
   

   ∴ R =	100 × S.I
   	P × T

   
   

   R =	100 × 156	= 13%
   	600 × 2

   
   Second method to solve this question :
   Here , A₂ = ₹ 873 , T₁ = 2 years , A₁ = ₹ 756 , T₂ = 3.5 years = 7 / 2 years
   

   Rate of interest =		A1 - A2		× 100
   		A2T1 - A1T2

   
   

   Rate of interest =		756 -873			× 100
   		873 ×2 - 756 ×	7
   			2

   
   

   Rate of interest =		- 117		× 100
   		1746 - 2646

   
   

   Rate of interest =		- 117		× 100 = 13%
   		- 900

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15. What sum will amount to 7000 in 5 years at 3	1	% simple inter- est ?
    	3

    
    

1. 1. 6300
      

   
   
   

   2. 6500
      

   
   
   

   3. 6000
      

   
   
   

   4. 5000

   
   
   

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1. View Hint View Answer Discuss in Forum

   Here , A = ₹ 7000 , T= 5 years , R =	10
   	3

   
   We find the required answer with the help of given formula ,
   

   P =	A × 100
   	100 + R × T

   
   

   Correct Option: C

   Here , A = ₹ 7000 , T= 5 years , R =	10
   	3

   
   We find the required answer with the help of given formula ,
   

   P =	A × 100
   	100 + R × T

   
   

   P =		7000 × 100
   	100 +	10	× 5
   		3

   
   

   P =	7000 × 100 × 3	= ₹ 6000
   	350

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