1.

Two years ago a man was five times as old as his son. Two years later his age will be 8 more than

Answer»

Given:-

  • Two years ago, a man was five times as old as his son.

  • Two years later,  his age will be 8 more than THREE times the age of the son.

To FIND out:-

Find the present ages of the man and his son.

Solution:-

Let the present age of his son be a.

Then, the present age of the father = b

According to the question,

★ Two years ago,

⇒( b - 2 ) = 5 ( a - 2 )

⇒ b - 2 = 5a - 10

 

⇒ b = 5a - 8 .......( 1 )

★ Two years later,

b + 2 = 8 + 3 ( a + 2 )

⇒ b + 2 = 8 + 3a + 6

⇒ b + 2 = 3a + 14

⇒ b = 3a + 12.......( 2 )

From ( 1 ) and ( 2 )

5a - 8 = 3a + 12

⇒ 5a - 3a = 12 + 8

⇒ 2a = 20

⇒ a = 10

Now,

Substituting the value of a in EQUATION ( 1 )

b = 5a - 8

b = 5 × 10 - 8

b = 50 - 8

b = 42

Hence,the present age of man and his son are 42 and 10 respectively.



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