Question

The difference between the ages of a mother and her daughter is 24 years .The sun of reciprocal of their ages is 1/9.Find the mother present age
​

Answer 1

Answer:

search-icon-image

Question

Bookmark

The difference of mother's age and her daughter's age is 24 years and the twelfth part of the product of their ages is less than the mother's age by 18 years.

Let the daughter's age be x years.

Hence, mother's age will be (x+21) years

Now,

12

x(21+x)

=x+21−18=x+3

∴x(21+x)=12x+36

∴21x+x

2

=12x+36

∴x

2

+9x−36=0

∴(x−3)(x+12)=0

Since age can only be positive, so x=3.

Thus mother's age is 21+3=24 years

Answer 2

Step-by-step explanation:

let the age of of the mother be x years then the age of her daughter will be (x-24) years

reciprocal of mother's age = 1/x years

reciprocal of daughter's age = 1/(x-24) years

A/Q = 1/x + 1/(x-24) = 1/9

= (x-24+ x)/x²-24x = 1/9

= 2x-24/x²-24x = 1/9

by cross multiplication

= 9(2x-24) = x²-24x

= 18x -216 = x² - 24x

= 42x -216 = x²

= x²-42x + 216 = 0

= x² -36x -6x + 216 = 0

= x(x-36) -6(x-36) = 0

= (x-6)(x-36) = 0

so the value of x will be 6 or 36

but we take x = mother's age so x= 36

so present age of mother = 36years

PLEASE MARK AS BRANLIEST