316. The ratio of two numbers is 4 : 5 when the first is increased by 20% and the second is decreased by 20%, the ratio of the resulting numbers is

1. 1. 4 : 5

   
   
   

   2. 5 : 4

   
   
   

   3. 5 : 6

   
   
   

   4. 6 : 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be 4k and m5k .
   After corresponding increase or decrease,
   

   Required ratio = 4k ×	120	: 5k ×	80
   	100		100

   
   

   Correct Option: D

   Let the numbers be 4k and m5k .
   After corresponding increase or decrease,
   

   Required ratio = 4k ×	120	: 5k ×	80
   	100		100

   
   Hence , Required ratio = 12k : 10k = 6 : 5

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317. Rama’s expenditures and savings are in the ratio 5 : 3. If her in- come increases by 12% and expenditure by 15%, then by how much per cent do her savings increase ?

1. 1. 12%

   
   
   

   2. 7%

   
   
   

   3. 8%

   
   
   

   4. 13%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let Rama’s expenditure = 5k
   Savings = 3k
   ∴ Rama’s income = 5k + 3k = 8k
   After increase,
   

   Rama’s income =	112	× 8k = 8.96 k
   	100

   
   

   Rama’s expenditure =	5k × 115	= 5.75k
   	100

   
   Rama’s savings = (8.96k – 5.75k) = 3.21k
   

   Correct Option: B

   Let Rama’s expenditure = 5k
   Savings = 3k
   ∴ Rama’s income = 5k + 3k = 8k
   After increase,
   

   Rama’s income =	112	× 8k = 8.96 k
   	100

   
   

   Rama’s expenditure =	5k × 115	= 5.75k
   	100

   
   Rama’s savings = (8.96k – 5.75k) = 3.21k
   

   ∴ Rama’s saving percent =			3.21k - 3k		× 100
   			3k

   
   

   Rama’s saving percent =	0.21	× 100 = 7%
   	3

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318. The price of sugar is increased by 20%. If the expenditure on sugar has to be kept the same as earlier, the ratio between the reduction in consumption and the original consumption is

1. 1. 1 : 3

   
   
   

   2. 1 : 4

   
   
   

   3. 1 : 6

   
   
   

   4. 1 : 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   The raised price =	120	of the former price
   	100

   
   

   ∴ The householder must now consume	100	of the original amount
   	120

   
   

   ∴ The reduction in consumption =		1 -	100		of the original consumption
   			120

   
   

   =	1	of the original consumption
   	6

   
   Required ratio = 1 : 6
   Second method to solve this question ,
   

   Required percentage =			20		× 100
   			100 + 20

   
   

   Correct Option: C

   The raised price =	120	of the former price
   	100

   
   

   ∴ The householder must now consume	100	of the original amount
   	120

   
   

   ∴ The reduction in consumption =		1 -	100		of the original consumption
   			120

   
   

   =	1	of the original consumption
   	6

   
   Required ratio = 1 : 6
   Second method to solve this question ,
   

   Required percentage =			20		× 100
   			100 + 20

   
   

   Required percentage =	20	× 100
   	120

   
   

   Required percentage =	100	%
   	6

   
   Required ratio = 1 : 6

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319. The difference of two numbers is 15% of their sum. The ratio of the larger number to the smaller number is

1. 1. 23 : 17

   
   
   

   2. 11 : 9

   
   
   

   3. 17 : 11

   
   
   

   4. 23 : 11

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the numbers be p and q
   where p > q. Then,
   

   p - q =	15	(p + q)
   	100

   
   

   ⇒ p - q =	3	(p + q)
   	20

   
   ⇒ 20p – 20q = 3p + 3q
   ⇒ 20p – 3p = 20q + 3q
   

   Correct Option: A

   Let the numbers be p and q
   where p > q. Then,
   

   p - q =	15	(p + q)
   	100

   
   

   ⇒ p - q =	3	(p + q)
   	20

   
   ⇒ 20p – 20q = 3p + 3q
   ⇒ 20p – 3p = 20q + 3q
   

   ⇒ 17p = 23q ⇒	p	=	23
   	q		17

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320. The bus fare and train fare of a place from Kolkata were 20 and 30 respectively. Train fare has been increased by 20% and the bus fare has been increased by 10%. The ratio of new train fare to new bus fare is

1. 1. 11 : 18

   
   
   

   2. 18 : 11

   
   
   

   3. 5 : 3

   
   
   

   4. 3 : 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Increased train fare = ₹		120	× 30		= ₹ 36
   		100

   
   

   Correct Option: B

   Increased train fare = ₹		120	× 30		= ₹ 36
   		100

   
   

   Increased bus fare = ₹		110	× 20		= ₹ 22
   		100

   
   ∴ Required ratio = 36 : 22 = 18 : 11

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