521. The average age of boys in the class is twice the number of girls in the class. The ratio of boys and girls in the class of 50 is 4 : 1. The total of the ages (in years) of the boys in the class is

1. 1. 2000

   
   
   

   2. 2500

   
   
   

   3. 800

   
   
   

   4. 400

   
   
   

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1. View Hint View Answer Discuss in Forum

   Boys in class =	4	× 50 = 40
   	5

   
   

   Girls =	1	× 50 = 10
   	5

   
   Average age of boys = 10 × 2
   = 20 years
   ∴  Total age of boys = 20 × 40
   = 800 years

   Correct Option: C

   Boys in class =	4	× 50 = 40
   	5

   
   

   Girls =	1	× 50 = 10
   	5

   
   Average age of boys = 10 × 2
   = 20 years
   ∴  Total age of boys = 20 × 40
   = 800 years

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522. Four years ago, the ratio of the age of A and B was 2 : 3 and after four years it will become
     5 : 7. Find their present age.

1. 1. 36 years and 40 years

   
   
   

   2. 32 years and 48 years

   
   
   

   3. 40 years and 56 years

   
   
   

   4. 36 years and 52 years

   
   
   

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1. View Hint View Answer Discuss in Forum

   Four years ago let the age of A and B be 2x and 3x years respectively.
   According to the question
   

   2x + 4 + 4	=	5
   3x + 4 + 4		7

   
   

   ⇒	2x + 8	=	5
   	3x + 8		7

   
   ⇒  14x + 56 = 15x + 40
   ⇒  x = 16
   Present age of A = 2x + 4
   = 2 × 16 + 4 = 36 years
   Present age of B
   = 3x + 4 = 3 × 16 + 4
   = 52 years

   Correct Option: D

   Four years ago let the age of A and B be 2x and 3x years respectively.
   According to the question
   

   2x + 4 + 4	=	5
   3x + 4 + 4		7

   
   

   ⇒	2x + 8	=	5
   	3x + 8		7

   
   ⇒  14x + 56 = 15x + 40
   ⇒  x = 16
   Present age of A = 2x + 4
   = 2 × 16 + 4 = 36 years
   Present age of B
   = 3x + 4 = 3 × 16 + 4
   = 52 years

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523. The ratio of present age of two brothers is 1 : 2 and 5 years back the ratio was 1 : 3. What
     will be the ratio of their age after 5 years ?

1. 1. 1 : 4

   
   
   

   2. 2 : 3

   
   
   

   3. 3 : 5

   
   
   

   4. 5 : 6

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the present age of two brothers be x and 2x years.
   

   Now,	x − 5	=	1
   	2x − 5		3

   
   ⇒  3x – 15 = 2x – 5
   ⇒  3x – 2x = 15 – 5
   ⇒  x= 10
   ∴  Their present age
   = 10 and 20 years
   After 5 years their required ratio
   

   =	15	=	3	= 3 : 5
   	25		5

   Correct Option: C

   Let the present age of two brothers be x and 2x years.
   

   Now,	x − 5	=	1
   	2x − 5		3

   
   ⇒  3x – 15 = 2x – 5
   ⇒  3x – 2x = 15 – 5
   ⇒  x= 10
   ∴  Their present age
   = 10 and 20 years
   After 5 years their required ratio
   

   =	15	=	3	= 3 : 5
   	25		5

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524. Harsha is 40 years old and Ritu is 60 years old. How many years ago was the ratio of their ages 3:5?

1. 1. 10 years

   
   
   

   2. 20 years

   
   
   

   3. 37 years

   
   
   

   4. 5 years

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let x years ago the ratio of their age was 3 : 5
   ∴  According to the question
   

   40 − x	=	3
   60 − x		5

   
   ⇒  200 – 5x = 180 – 3x
   ⇒  2x = 20
   ∴  x = 10 years

   Correct Option: A

   Let x years ago the ratio of their age was 3 : 5
   ∴  According to the question
   

   40 − x	=	3
   60 − x		5

   
   ⇒  200 – 5x = 180 – 3x
   ⇒  2x = 20
   ∴  x = 10 years

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525. The ratio between Sumit’s and Prakash’s age at present is 2 : 3. Sumit is 6 years younger than Prakash. The ratio of Sumit’s age to Prakash’s age after 6 years will be

1. 1. 2 : 3

   
   
   

   2. 1 : 2

   
   
   

   3. 4 : 3

   
   
   

   4. 3 : 4

   
   
   

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1. View Hint View Answer Discuss in Forum

   Sumit’s present age = 2x years
   Prakash’s present age = 3x years
   ∴  3x– 2x = 6
   x = 6
   ∴  Required ratio
   = (2 × 6 + 6) : (3 × 6 + 6)
   = 18 : 24 = 3 : 4

   Correct Option: D

   Sumit’s present age = 2x years
   Prakash’s present age = 3x years
   ∴  3x– 2x = 6
   x = 6
   ∴  Required ratio
   = (2 × 6 + 6) : (3 × 6 + 6)
   = 18 : 24 = 3 : 4

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