Question

4. Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son. Find their present ages ten years ago.​

Answer 1

Given : Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son.  

 

To Find :Their present ages  [Mistake in the question]

Solution:  

Let the ages of a man and his son be x yrs and y yrs.

For Case I :

Six years hence a man's age will be three times the age of his son.

x + 6 = 3(y + 6)

x + 6 = 3y + 18

x = 3y + 18 - 6

x = 3y + 12 ……………..(1)

 

For Case II :

Three years ago he was nine times as old as his son.

x - 3 = 9(y - 3)

On putting the value of x from equation (1)

3y + 12 - 3 = 9y - 27

3y - 9y = -27 + 3 - 12

-6y = -36

6y = 36

y = 36/6  

y = 6

On putting the value of y in equation (1) we get,

x = 3y + 12

x = 3 × 6 + 12  

x = 18 + 12

x = 30

Hence, the age of a man and his son are 30 years and 6 years .

 

Learn more :  

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

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Five years hence, a man's age will be three times the age of his son. Five years ago, the man was seven times as old as his son. Find their present age.

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Answer 2

Answer :-

Given : Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son.  

 

To Find :Their present ages  [Mistake in the question]

Solution:  

Let the ages of a man and his son be x yrs and y yrs.

For Case I :

Six years hence a man's age will be three times the age of his son.

x + 6 = 3(y + 6)

x + 6 = 3y + 18

x = 3y + 18 - 6

x = 3y + 12 ……………..(1)

 

For Case II :

Three years ago he was nine times as old as his son.

x - 3 = 9(y - 3)

On putting the value of x from equation (1)

3y + 12 - 3 = 9y - 27

3y - 9y = -27 + 3 - 12

-6y = -36

6y = 36

y = 36/6  

y = 6

On putting the value of y in equation (1) we get,

x = 3y + 12

x = 3 × 6 + 12  

x = 18 + 12

x = 30

Hence, the age of a man and his son are 30 years and 6 years .