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Answers
Topic - Finding Ages
Assumption:
- Let, mother be x years old
- and daughter be y years old.
Given:
- The difference of their ages is 21 years:
- x - y = 21 ....(i)
- The twelfth part of the product of their ages is less than the mother's age by 18 years:
- 1/12 * (xy) = x - 18 .....(ii)
- From (i), we get y = x - 21
- Putting y = x - 21 in (ii), we get
- 1/12 * x (x - 21) = x - 18
- or, x² - 21x = 12x - 216
- or, x² - 33x + 216 = 0
- or, x² - 24x - 9x + 216 = 0
- or, x (x - 24) - 9 (x - 24) = 0
- or, (x - 24) (x - 9) = 0
- ∴ either x = 24 or x = 9.
We take x = 24 because x = 9 is not acceptable.
From (i), we get by putting x = 24,
- 24 - y = 21
- or, y = 24 - 21
- or, y = 3
Answer:
- Age of the mother is 24 years.
- Age of the daughter is 3 years.
Solution
Given:-
- Difference of mother's age and her daughter's age = 21 years
- Twelfth part of the product of their ages is less than the mother's age by 18 years.
Find:-
- Age of mother and her daughter .
Explanation:-
Let,
- Age of mother = x years
- Age of daughter = y Years
A/C to question,
(Difference of mother's age and her daughter's age = 21 years)
➠ x - y = 21 ........(1)
Again,
( Twelfth part of the product of their ages is less than the mother's age by 18 years.)
➠1/12 × (x.y) = x - 18
➠ x.y = 12(x-18)
keep value of y in equ(1),
➠ x.(x-21) = 12(x-18)
➠x² - 21x - 12x + 216 = 0
➠x² - 33x + 216 = 0
➠x² - 24x - 9x + 216 = 0
➠ x(x-24)-9(x-24) = 0
➠(x-24)(x-9) = 0
➠(x-24) = 0. Or, (x-9) = 0
➠ x = 24. Or, x = 9
Keep value of x in equ(1),
When
- x = 24
➠24 - y = 21
➠ y = 24 - 21
➠y = 3
when,
- x = 9
➠ 9 - y = 21
➠ y = 9 + 21
➠y = 30
Here, when mother was 24 years then her daughter's age was 3 years
And, when mother's age was 9 years then her daughter's age was = 30 years .
So , this is not possible , because mother's age is always greater than her daughter's age .
So, x = 9, y = 30 is not acceptable values
Thus:-
- Age of mother's (x) = 24 years
- Age of her daughter's (y) = 3 years .