Question

the sum of the ages of sanjay and vijay is thrice the sum of their ages 5 yrs ago. what is the product of their present age, if the sum of the squares of thir ages 5 yrs ago was 100?​

Answer 1

Answer:

12.5 years

Step-by-step explanation:

as attached with this solution

Answer 2

The sum of the ages of Sanjay and Vijay is thrice the sum of their ages 5 yrs ago

Let the present age of Sanjay be x

Present age of Vijay be y

Five years ago ,

Age of Sanjay = x - 5

Age of Vijay = y - 5

➠ x + y = = 3 [ (x - 5) + (y - 5) ]

➠ x + y = 3 [ x - 5 + y - 5 ]

➠ x + y = 3 [ x + y - 10 ]

➠ x + y = 3x + 3y - 30

➠ 3x + 3y - x - y = 30

➠ 2x + 2y = 30

➠ x + y = 15  ... (1)

The sum of the squares of their ages 5 yrs ago was 100

➳ ( x - 5 )² + ( y - 5 )² = 100

➳ x² + 25 - 10x + y² + 25 - 10y = 100

➳ x² + y² - 10x - 10y + 50 = 100

➳ x² + y² - 10x - 10y = 100 - 50

➳ x² + y² - 10 ( x + y ) = 50

➳ x² + y² - 10 ( 15 ) = 50  [ From (1) ]

➳ x² + y² - 150 = 50

➳ x² + y² = 200

• ( a + b )² = a² + b² + 2ab

⇒ a² + b² = ( a + b )² - 2ab

➳ ( x + y )² - 2xy = 200

➳ ( 15 )² - 2xy = 200  [ From (1) ]

➳ 225 - 200 = 2xy

➳ 2xy = 25

➳ xy = 25/2

➳ xy = 12.5 years  $\orange{\bigstar}$

Product of their present ages is 12.5 years