Dhwani age at present is 2 year less then 6 times the age of here soon amar.the product of their ages 5 years later will be 33/. what was the age of dhwani when her son Amar was born
Answers
Dhwani age at present is 2 year less then 6 times the age of here soon amar.the product of their ages 5 years later will be 330.Age of dhwani was 23 years old when her son Amar was born
Let us consider the present age of Dhwani be 'x' years and her son Amar be 'y' years.
Given that, Dhwani’s present age is 2 years less than 6 times her son Amar. We represent the above statement in equation as:
x = 6y – 2 ..(1)
After 5 years:
Amar’s age = (y + 5) years
Dhwani’ age = (x + 5) years
Replacing the value of x from (1),
Age = (6y – 2 + 5)
= (6y + 3) years
Again, it is given that tthe product of their ages is 330.
So,
[(y+5)*(6y+3)] = 330
⇒ 6y² + 3y + 30y + 15 = 330
⇒ 6y² + 33y – 315 = 0
⇒ 2y² + 11y – 105 = 0 [dividing by 3 on both sides]
⇒ 2y² + 21y – 10y – 105 = 0
⇒ 2y(y+10.5) – 10(y+10.5) = 0
⇒ (y+10.5)(2y-10) = 0
By zero product's rule, we get
y = 10/2 = 5, as age cannot be negative.
x = 6y + 3 according to eqn.(1).
x = 6(5) + 3 = 30 + 3
= 33years
So, when Amar was born Dhwani was (28-5) = 23 years old.