56. A sum was invested on simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched ₹72 more. The sum is
    

1. 1. ₹1,200
      

   
   
   

   2. ₹1,500
      

   
   
   

   3. ₹1,600
      

   
   
   

   4. ₹1,800

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the sum = P and original rate = R% per annum.
   Then,
   According to question ,
   

   P × (R + 3) × 2	-	P × R × 2	= 72
   100		100

   
   

   ⇒	P × 3 × 2	= 72
   	100

   
   

   ⇒ P =	72 × 100	= ₹ 1200
   	3 × 2

   
   Second method to solve this question :
   Here , P₁ = P, R₁ = R, T₁ = 2
   P₂ = P, R₂ = R + 3, T₂ = 2 , S.I.= 72
   

   ∴ SI =	P2 × R2 × T2 - P1 × R1 × T1
   	100

   
   

   Correct Option: A

   Let the sum = P and original rate = R% per annum.
   Then,
   According to question ,
   

   P × (R + 3) × 2	-	P × R × 2	= 72
   100		100

   
   

   ⇒	P × 3 × 2	= 72
   	100

   
   

   ⇒ P =	72 × 100	= ₹ 1200
   	3 × 2

   
   Second method to solve this question :
   Here , P₁ = P, R₁ = R, T₁ = 2
   P₂ = P, R₂ = R + 3, T₂ = 2 , S.I.= 72
   

   ∴ SI =	P2 × R2 × T2 - P1 × R1 × T1
   	100

   
   

   72 =	P × (R + 3) × 2 - P × R × 2
   	100

   
   7200 = 6P
   P = ₹ 1200

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57. If the annual rate of simple interest increases from 10% to 12	1	%, a man’s yearly
    	2

    income increases by ₹1250. His principal (in rupees) is
    

1. 1. 50,000
      

   
   
   

   2. 45,000
      

   
   
   

   3. 60,000
      

   
   
   

   4. 65,000

   
   
   

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1. View Hint View Answer Discuss in Forum

   As per the given in question,
   

   Change in SI =		25	- 10		% =	5	%
   		2				2

   
   

   ∴	5	% of principal = ₹ 1250
   	2

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

   Principal =	SI × 100
   	R × T

   
   

   Correct Option: A

   As per the given in question,
   

   Change in SI =		25	- 10		% =	5	%
   		2				2

   
   

   ∴	5	% of principal = ₹ 1250
   	2

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

   Principal =	SI × 100
   	R × T

   
   

   ∴ Principal = ₹	1250 × 2 × 100	= ₹ 50000
   	5

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58. A sum of ₹400 amounts to ₹480 in 4 years. What will it amount to if the rate of interest is increased by 2%?
    

1. 1. ₹484
      

   
   
   

   2. ₹560
      

   
   
   

   3. ₹512
      

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given that , Principal = ₹ 400 and Amount = ₹ 480
   Simple Interest = Amount - Principal = ₹(480 – 400) = ₹80
   As we know that ,
   

   SI =	P × R × T
   	100

   
   

   ∴ 80 =	400 × r × 4	⇒ r = 5
   	100

   
   Now, r = 7% (2% increase)
   

   Correct Option: C

   Given that , Principal = ₹ 400 and Amount = ₹ 480
   Simple Interest = Amount - Principal = ₹(480 – 400) = ₹80
   As we know that ,
   

   SI =	P × R × T
   	100

   
   

   ∴ 80 =	400 × r × 4	⇒ r = 5
   	100

   
   Now, r = 7% (2% increase)
   

   ∴ S.I =	400 × 7 × 4	= 112
   	100

   
   ∴ Amount = Principal + SI = ₹ (400 + 112) = ₹ 512

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59. A sum of Rs. 4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. If the annual interest is Rs. 352, the sum lent at 8% is
    

1. 1. Rs. 2900
      

   
   
   

   2. Rs. 2200
      

   
   
   

   3. Rs. 2400
      

   
   
   

   4. Rs. 3100

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let Principal lent at 8% S.I. = Rs. p.
   ∴ Principal lent at 10% S.I. = Rs. (4000 – p)
   We know that ,
   

   S.I =	Principal × Time × Rate
   	100

   
   From the question ,
   

   ∴	p × 8	+	(4000 - p) × 10	= 352
   	100		100

   
   

   Correct Option: C

   Let Principal lent at 8% S.I. = Rs. p.
   ∴ Principal lent at 10% S.I. = Rs. (4000 – p)
   We know that ,
   

   S.I =	Principal × Time × Rate
   	100

   
   From the question ,
   

   ∴	p × 8	+	(4000 - p) × 10	= 352
   	100		100

   
   ⇒ 8p + 40000 – 10p = 35200
   ⇒ 2p = 40000 – 35200 = 4800
   

   ⇒ p =	4800	= Rs. 2400
   	2

   
   

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60. If the ratio of principal and the simple interest for 5 years is 10 : 3, then the rate of interest is :
    

1. 1. 5%
      

   
   
   

   2. 6%
      

   
   
   

   3. 8%
      

   
   
   

   4. 3%

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question ,
   

   Principal	=	10
   Interest		3

   
   

   ⇒	Interest	=	3
   	Principal		10

   
   

   ∴ Rate =	Simple Interest × 100
   	Principal × Time

   
   

   Correct Option: B

   According to question ,
   

   Principal	=	10
   Interest		3

   
   

   ⇒	Interest	=	3
   	Principal		10

   
   

   ∴ Rate =	Simple Interest × 100
   	Principal × Time

   
   

   Rate =	3	×	100	= 6% per annum
   	10		5

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