21. If a sum of money amounts to ₹12,900 and ₹14,250 at the end of 4th year and 5th year respectively at a certain rate of simple interest, then the rate of interest is
    

1. 1. 10%
      

   
   
   

   2. 12%
      

   
   
   

   3. 18%
      

   
   
   

   4. 20%

   
   
   

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1. View Hint View Answer Discuss in Forum

   SI = Amount - Principle
   S.I. for 1 year = 14250 – 12900 = Rs. 1350
   S.I. for 4 years = 1350 × 4 = ₹ 5400
   ∴ Principal = 12900 – 5400 = ₹ 7500
   

   ∴ Rate =	SI × 100
   	Principal × Time

   
   

   Rate =	5400 × 100
   	7500 × 4

   
   Rate = 18% per annum
   Second method to solve this question :
   Here , A₂ = ₹ 14250 , T₁ = 4 years , A₁ = ₹ 12900 , T₂ = 5 years
   

   R =		A1 - A2		× 100
   		A2T1 - A1T2

   
   

   Correct Option: C

   SI = Amount - Principle
   S.I. for 1 year = 14250 – 12900 = Rs. 1350
   S.I. for 4 years = 1350 × 4 = ₹ 5400
   ∴ Principal = 12900 – 5400 = ₹ 7500
   

   ∴ Rate =	SI × 100
   	Principal × Time

   
   

   Rate =	5400 × 100
   	7500 × 4

   
   Rate = 18% per annum
   Second method to solve this question :
   Here , A₂ = ₹ 14250 , T₁ = 4 years , A₁ = ₹ 12900 , T₂ = 5 years
   

   R =		A1 - A2		× 100
   		A2T1 - A1T2

   
   

   R =		12900 - 14250		× 100
   		14250 × 4 - 12900 × 5

   
   

   R =	- 1350	× 100
   	57000 - 64500

   
   

   R =	1350	× 100
   	7500

   
   R = 18%

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22. In what time will ₹8,000, at 3% per annum, produce the same interest as ₹6, 000 does in 5 years at 4 % simple interest ?
    

1. 1. 5 years
      

   
   
   

   2. 6 years
      

   
   
   

   3. 3 years
      

   
   
   

   4. 4 years

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let Required time = t years
   We know that ,
   

   SI =	Principal × Time × Rate
   	100

   
   

   ∴	6000 × 4 × 5	=	8000 × 3 × t
   	100		100

   
   ⇒ 6000 × 4 × 5 = 8000 × 3 × t
   

   Correct Option: A

   Let Required time = t years
   We know that ,
   

   SI =	Principal × Time × Rate
   	100

   
   

   ∴	6000 × 4 × 5	=	8000 × 3 × t
   	100		100

   
   ⇒ 6000 × 4 × 5 = 8000 × 3 × t
   

   ∴ t =	6000 × 4 × 5
   	8000 × 3

   
   t = 5 years

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23. The sum of money that will yield Rs. 60 as simple interest at the rate of 6% per annum in 5 years is
    

1. 1. 200
      

   
   
   

   2. 225
      

   
   
   

   3. 175
      

   
   
   

   4. 300

   
   
   

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1. View Hint View Answer Discuss in Forum

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

   Principal =	S.I × 100
   	Time × Rate

   
   

   Correct Option: A

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

   Principal =	S.I × 100
   	Time × Rate

   
   

   Principal =	60 × 100	= Rs. 200
   	5 × 6

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24. If a sum of money becomes Rs. 4000 in 2 years and Rs. 5500 in 4 years 6 months at the same rate of simple interest per annum, then the rate of simple interest is

1. 1. 21	3	%
      	7

   
   
   

   2. 21	2	%
      	7

   
   
   

   3. 21	1	%
      	7

   
   
   

   4. 21	5	%
      	7

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to the question,
   S.I. for 2 years 6 months = Rs. (5500 – 4000)
   

   ⇒ S.I. for	5	years = Rs. 1500
   	2

   
   

   ∴ S.I. for 1 year =	1500 × 2	= Rs. 600
   	5

   
   ∴ S.I. for 2 years = Rs. 1200
   ∴ Principal = Amount - SI = Rs. (4000 – 1200) = Rs. 2800
   

   ∴ Rate =	SI × 100
   	Principal × Time

   
   

   Correct Option: A

   According to the question,
   S.I. for 2 years 6 months = Rs. (5500 – 4000)
   

   ⇒ S.I. for	5	years = Rs. 1500
   	2

   
   

   ∴ S.I. for 1 year =	1500 × 2	= Rs. 600
   	5

   
   ∴ S.I. for 2 years = Rs. 1200
   ∴ Principal = Amount - SI = Rs. (4000 – 1200) = Rs. 2800
   

   ∴ Rate =	SI × 100
   	Principal × Time

   
   

   Rate =	1200 × 100	=	150
   	2800 × 2		7

   
   

   Rate = 21	3	% per annum.
   	7

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25. The simple interest on a certain sum of money at the rate of 5% per annum for 8 years is Rs. 840. Rate of interest for which the same amount of interest can be received on the same sum after 5 years is :
    

1. 1. 7% per annum
      

   
   
   

   2. 8% per annum
      

   
   
   

   3. 9% per annum
      

   
   
   

   4. 10% per annum

   
   
   

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1. View Hint View Answer Discuss in Forum

   Case I,
   

   Principal =	SI × 100
   	Time × Rate

   
   

   =	840 × 100	= Rs. 2100
   	8 × 5

   
   Case II,
   S.I. = Rs. 840 , Principal = Rs. 2100 , Time = 5 years
   We know that ,
   

   Rate =	SI × 100
   	Principal × Time

   
   

   Correct Option: B

   Case I,
   

   Principal =	SI × 100
   	Time × Rate

   
   

   =	840 × 100	= Rs. 2100
   	8 × 5

   
   Case II,
   S.I. = Rs. 840 , Principal = Rs. 2100 , Time = 5 years
   We know that ,
   

   Rate =	SI × 100
   	Principal × Time

   
   

   Rate =	840 × 100	= 8% per annum
   	2100 × 5

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