Dhwani's age at present is 2 years less then 6 times the age of her son amar. The product of their ages 5 years later will be 330. What is the age of Dhawni when her son was born?
Answers
The age of Dhawni when her son was born was 23 years.
Step-by-step explanation:
Let the present age of Dhwani be “x” years and her son Amar be “y” years.
It is given that Dhwani’s present age is 2 years less than 6 times her son Amar’s age, so, we have the equation as,
x = 6y – 2
Now,
After 5 years:
Amar’s age = (y + 5) years
Dhwani’ age = x + 5 = 6y – 2 + 5 = (6y + 3) years
According to the question, we get the equation as,
(y+5) * (6y+3) = 330
⇒ 6y² + 3y + 30y + 15 = 330
⇒ 6y² + 33y – 315 = 0
⇒ 2y² + 11y – 105 = 0 ….. [dividing by 3 throughout]
⇒ 2y² + 21y – 10y – 105 = 0
⇒ 2y(y+10.5) – 10(y+10.5) = 0
⇒ (y+10.5)(2y-10) = 0
⇒ y = -10.5 or y = 10/2 = 5
(neglecting the negative value)
⇒ y = 5 years ← Amar’s present age
∴ x = 6*5 – 2 = 30 – 2 = 28 years ← Dhwani’s present age
Thus,
Dhwani’s age when her son was born will be = 28 – 5 = 23 years
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