Question

The sum of the ages of a woman and her daughter is 46years In 4 years time,the ratio of their ages will be 7:2. Find their present ages

Answer 1

Given :

• The sum of the ages of a woman and her daughter is 46 years.
• In 4 years time,the ratio of their ages will be 7:2.

To find :

• Their present ages.

Solution :

Consider,

• Present age of woman = x years
• Present age of Daughter = y years

According to the 1st condition :-

• The sum of the ages of a woman and her daughter is 46 years.

$\to\sf{x+y=46}$

$\to\sf{x=46-y.................(1)}$

According to the 2nd condition :-

• In 4 years time,the ratio of their ages will be 7:2.

After 4 years,

• Age of woman = (x+4) years
• Age of daughter = (y+4) years

→ (x+4) : (y +4) = 7:2

→ x+4/y+4 = 7/2

→ 46-y+4/y+4 = 7/2

→ 50-y/y+4 = 7/2

→7y +28 = 100-2y

→ 7y +2y = 100 -28

→ 9y = 72

→ y = 8

• Present age of Daughter = 8 years.

Now put y = 8 in eq(1) .

→ x = 46 - y

→ x = 46 - 8

→ x = 38

• Present age of woman = 38 years.

Answer 2

Answer:

Let the Age of Woman be n and Age of Daughter be (46 - n) i.e. sum is 46 years

⠀

☆ Given : In 4 years time, the ratio of their ages will be 7 : 2

⠀

☯ $\underline{\boldsymbol{According\: to \:the\: Question :}}$

$:\implies\sf Woman: Daughter=7:2\\\\\\:\implies\sf \dfrac{n+4}{(46-n)+4}=\dfrac{7}{2}\\\\\\:\implies\sf \dfrac{n+4}{46-n+4}=\dfrac{7}{2}\\\\\\:\implies\sf \dfrac{n+4}{50-n}=\dfrac{7}{2}\\\\\\:\implies\sf (n + 4) \times 2 = 7(50 - n)\\\\\\:\implies\sf 2n + 8 = 350 - 7n\\\\\\:\implies\sf 2n + 7n = 350 - 8\\\\\\:\implies\sf 9n =342\\\\\\:\implies\sf n = \dfrac{342}{9}\\\\\\:\implies\sf n = 38 \:years\qquad\bigg\lgroup\bf Woman's\:\: Age\bigg\rgroup$

⠀⠀⠀$\rule{160}{1}$

$:\implies\sf Daughter=(46-n)\\\\\\:\implies\sf Daughter=(46-38)\\\\\\:\implies\sf Daughter=8\:years\qquad\bigg\lgroup\bf Daughter's\:\:Age\bigg\rgroup$