In a family of four persons, the father’s age is 8 times the age of the daughter. The son is half as old as his mother and is 15 years older than his sister. If the father is 12 years older than his wife, what is the mother’s age?

Solution

Let the mother’s age = [if gte msEquation 12]>x [if !msEquation]-->[endif]-->`x` years , Father’s age = ( [if gte msEquation 12]>x [if !msEquation]-->`x` + 12) years Age of the daughter =(`(x+12)/8` ) years Age of the son = [( ` (x+12)/8` ) + 15 ] = `(x+12+120)/8` years` ` As per the question, son’s age is half of that of his mother, Age of the son =` x/2` [if gte msEquation 12]> x 2 [if !msEquation]-->[endif]-->years `x/2=(x+12+120)/8` ⟹ 8`x` = 2 `x` + 24+ 240 ⟹ 8`x` - 2`x` = 24 + 240 ∴ 6 `x` = 264 years ∴ `x` = 44 years.