Question

Five year hence, father's age will be 3 times the age of his son. five years ago, father was seven times as old as his son. the age of the son at present is:

Answer 1

Let the father's age be x
and son's age be y

After five years ,

Father's age :- x + 5
Son's age :- y + 5

x + 5 = 3 ( y + 5 )

x + 5 = 3y + 15

x - 3y + 5 - 15 = 0

x - 3y - 10 = 0 .... ( i )



Before five years ,

Father's age :- x - 5
Son's age :- y - 5


x - 5 = 7 ( y - 5 )

x - 5 = 7y - 35

x - 7y - 5 + 35 = 0

x - 7y + 30 = 0 ..... ( ii )


Sub ( ii ) from ( i )

x - 3y - 10 - ( x - 7y + 30 ) = 0

x - 3y - 10 - x + 7y - 30 = 0

4y - 40 = 0

4y = 40

y = 10


Putting in ( i )

x - 3y - 10 = 0

x - 3 × 10 - 10 = 0

x - 30 - 10 = 0

x = 40


Father's age :- 40 years

Son's age :- 10 years .

Answer 2

Answer:

Step-by-step explanation:

Let seven years, age of Swati was x years and age of Varun was 5x² years

Present age of Swati = ( x + 7 ) years

Present age of Varun = ( 5x² + 7 ) years

Given, after 3 years swati's age will be 2 / 5 of Varun's age.

Age of Swati after 3 years = ( x + 7 + 3 ) years = ( x + 10 ) years

Age of Varun after 3 years = ( 5x² + 7 + 3 ) years = ( 5x² + 10 ) years

Given, age of Swati after 3 years = age of varun after 3 years

( x + 10 ) = 2 / 5 × ( 5x² + 10 )

( x + 10 ) = 2( x² + 2 )

x + 10 = 2x² + 4

2x² - x + 4 - 10 = 0

2x² - x - 6 = 0

2x² - 4x + 3x - 6 = 0

2x( x - 2 ) + 3( x - 2 ) = 0

x = 2 [ Age can't be negative ]

Therefore,

present age of Swati = ( 2 + 7 ) = 9 years

present age of Varun = 5(2)²+7=27 years

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