496. In an election, a candidate secures 40% of the votes but is defeated by the only other candidate by a majority of 298 votes. Find the total number of votes recorded.

1. 1. 1580

   
   
   

   2. 1490

   
   
   

   3. 1470

   
   
   

   4. 1530

   
   
   

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1. View Hint View Answer Discuss in Forum

   Total votes polled = x
   According to the question,
   (60 – 40)% of x = 298
   

   ⇒ x ×	20	= 298
   	100

   
   

   ⇒	x	= 298
   	5

   
   ⇒ x = 298 × 5 = 1490

   Correct Option: B

   Total votes polled = x
   According to the question,
   (60 – 40)% of x = 298
   

   ⇒ x ×	20	= 298
   	100

   
   

   ⇒	x	= 298
   	5

   
   ⇒ x = 298 × 5 = 1490

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497. The present population of a city is 180000. If it increases at the rate of 10% per annum, its population after 2 years will be :

1. 1. 207800

   
   
   

   2. 227800

   
   
   

   3. 217800

   
   
   

   4. 237800

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 17,
   Required population after two years
   

   = 180000		1 +	10		2
   			100

   
   

   = 180000 ×	11	×	11	= 217800
   	10		10

   Correct Option: C

   Using Rule 17,
   Required population after two years
   

   = 180000		1 +	10		2
   			100

   
   

   = 180000 ×	11	×	11	= 217800
   	10		10

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498. The value of an equipment depreciates by 20% each year. How much less will the value of the equipment be after 3 years ?

1. 1. 48.8%

   
   
   

   2. 51.2%

   
   
   

   3. 54%

   
   
   

   4. 60%

   
   
   

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1. View Hint View Answer Discuss in Forum

   If the present worth of the equipment be ₹ 100, then its price after 3 years
   

   = 100 ×			80		3	= ₹ 51.2
   			100

   
   ∴ Depriciation = 48.8%
   Aliter : Using Rule 18,
   Let the price of equipment be ₹ 100
   Its price after 3 years
   

   = 100		1 -	20		3
   			100

   
   

   = 100 ×			80		3	= ₹ 51.2
   			100

   
   Depriciation = 48.8%

   Correct Option: A

   If the present worth of the equipment be ₹ 100, then its price after 3 years
   

   = 100 ×			80		3	= ₹ 51.2
   			100

   
   ∴ Depriciation = 48.8%
   Aliter : Using Rule 18,
   Let the price of equipment be ₹ 100
   Its price after 3 years
   

   = 100		1 -	20		3
   			100

   
   

   = 100 ×			80		3	= ₹ 51.2
   			100

   
   Depriciation = 48.8%

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499. A district has 64000 inhabitants. If the population increases at
     

     the rate of 2	1	% per annum,
     	2

     
     the number of inhabitants at the end of 3 years will be

1. 1. 70000

   
   
   

   2. 69200

   
   
   

   3. 68921

   
   
   

   4. 68911

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 17,
   

   P = P0		1 +	R		T
   			100

   
   

   = 64000		1 +	5		3
   			200

   
   

   = 64000			41		3
   			40

   
   

   =	64000 × 41 × 41 × 41	= 68921
   	40 × 40 × 40

   
   

   Correct Option: C

   Using Rule 17,
   

   P = P0		1 +	R		T
   			100

   
   

   = 64000		1 +	5		3
   			200

   
   

   = 64000			41		3
   			40

   
   

   =	64000 × 41 × 41 × 41	= 68921
   	40 × 40 × 40

   
   

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500. The value of a property depreciates every year by 10% of its value at the beginning of the year. The present value of the property is ₹ 8100. What was its value 2 years ago ?

1. 1. ₹ 10,000

   
   
   

   2. ₹		90		2	× 8100
      		100

   
   
   

   3. ₹		100		2	× 8100
      		110

   
   
   

   4. ₹ 9801

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 18,
   Suppose the value of property two years ago was ₹ x
   According to question
   

   ∴ x		1 -	10		2	= 8100
   			100

   
   

   ⇒ x			90		2	= 8100
   			100

   
   

   =	8100 × 10 × 10	= ₹ 10000
   	9 × 9

   
   

   Correct Option: A

   Using Rule 18,
   Suppose the value of property two years ago was ₹ x
   According to question
   

   ∴ x		1 -	10		2	= 8100
   			100

   
   

   ⇒ x			90		2	= 8100
   			100

   
   

   =	8100 × 10 × 10	= ₹ 10000
   	9 × 9

   
   

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