561. In a factory, the production of cycles rose to 48, 400 from 40,000 in 2 years. The rate of growth per annum is

1. 1. 9%

   
   
   

   2. 8%

   
   
   

   3. 10.5%

   
   
   

   4. 10%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 17,
   If the rate of increase per annum be R%, then
   

   A = P		1 +	R		T
   			100

   
   

   ⇒ 48400 = 40000		1 +	R		2
   			100

   
   

   ⇒	484	=		1 +	R		2
   	100				100

   
   

   ⇒	121	=		11		2	=		1 +	R		2
   	100			10						100

   
   

   ⇒ 1 +	R	=	11
   	100		10

   
   

   ⇒	R	=	11	- 1 =	1
   	100		10		10

   
   

   ⇒ R =	100	= 10% per annum
   	10

   Correct Option: D

   Using Rule 17,
   If the rate of increase per annum be R%, then
   

   A = P		1 +	R		T
   			100

   
   

   ⇒ 48400 = 40000		1 +	R		2
   			100

   
   

   ⇒	484	=		1 +	R		2
   	100				100

   
   

   ⇒	121	=		11		2	=		1 +	R		2
   	100			10						100

   
   

   ⇒ 1 +	R	=	11
   	100		10

   
   

   ⇒	R	=	11	- 1 =	1
   	100		10		10

   
   

   ⇒ R =	100	= 10% per annum
   	10

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562. The present price of a scooter is Rs. 7,290. If its value decreases every year by 10%, then its value 3 years back was

1. 1. Rs. 10, 500

   
   
   

   2. Rs. 8,000

   
   
   

   3. Rs. 10,000

   
   
   

   4. Rs. 11,500

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 18,
   

   A = P		1 -	R		3
   			100

   
   

   ⇒ 7290 = P		1 -	10		3	= P		9		3
   			100					10

   
   

   ⇒ 7290 = P ×	9	×	9	×	9
   	10		10		10

   
   

   ⇒ P =	7290 × 10 × 10 × 10	= Rs. 10000
   	9 × 9 × 9

   
   

   Correct Option: C

   Using Rule 18,
   

   A = P		1 -	R		3
   			100

   
   

   ⇒ 7290 = P		1 -	10		3	= P		9		3
   			100					10

   
   

   ⇒ 7290 = P ×	9	×	9	×	9
   	10		10		10

   
   

   ⇒ P =	7290 × 10 × 10 × 10	= Rs. 10000
   	9 × 9 × 9

   
   

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563. The population of a town increases by 5% every year. If the present population is 9261, the population 3 years ago was

1. 1. 8000

   
   
   

   2. 5700

   
   
   

   3. 6000

   
   
   

   4. 7500

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 17,
   

   P = P0		1 +	R		T
   			100

   
   

   ⇒ 9261 = P0		1 +	5		3
   			100

   
   

   ⇒ 9261 = P0		1 +	1		3
   			20

   
   

   ⇒ 9261 = P0			21		3
   			20

   
   

   ⇒ P0 =	9261 × 20 × 20 × 20	= 8000
   	21 × 21 × 21

   Correct Option: A

   Using Rule 17,
   

   P = P0		1 +	R		T
   			100

   
   

   ⇒ 9261 = P0		1 +	5		3
   			100

   
   

   ⇒ 9261 = P0		1 +	1		3
   			20

   
   

   ⇒ 9261 = P0			21		3
   			20

   
   

   ⇒ P0 =	9261 × 20 × 20 × 20	= 8000
   	21 × 21 × 21

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564. An epidemic broke out in a village in which 5% of the population died. Of the remaining, 20% fled out of panic. If the present population is 4655, then the population of the village originally was

1. 1. 6000

   
   
   

   2. 6125

   
   
   

   3. 5955

   
   
   

   4. 5995

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 28,
   Original population of village = x (let)
   According to the question,
   

   x ×	95	×	80	= 4655
   	100		10

   
   

   ⇒ x =	4655 × 100 × 100	= 6125
   	95 × 80

   Correct Option: B

   Using Rule 28,
   Original population of village = x (let)
   According to the question,
   

   x ×	95	×	80	= 4655
   	100		10

   
   

   ⇒ x =	4655 × 100 × 100	= 6125
   	95 × 80

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565. The population of a town is 9000. It the number of females increases by 5% and the males by 7.5%, what will be the total population after increase. The number of females currently is 3000.

1. 1. 9600

   
   
   

   2. 9200

   
   
   

   3. 10500

   
   
   

   4. 9540

   
   
   

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1. View Hint View Answer Discuss in Forum

   In the village,
   Females = 3000
   Males = 9000 – 3000 = 6000
   After respective increases,
   Population of village
   

   = 3000 ×	105	+	6000 × 1075	= 4655
   	100		10

   
   = 3150 + 6450 = 9600

   Correct Option: A

   In the village,
   Females = 3000
   Males = 9000 – 3000 = 6000
   After respective increases,
   Population of village
   

   = 3000 ×	105	+	6000 × 1075	= 4655
   	100		10

   
   = 3150 + 6450 = 9600

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