Question

three years ago the age of the mother was 5 times the age of her daughter and two years hence she will be twice as old as her daughter will be fine present age​

Answer 1

Correct Question :-

Three years ago the age of mother was five times the age of her daughter and two years hence she will be thrice as old as her daughter will be. find their present ages.. ?

• 3 years ago , Mother = 5 * Daughter
• 2 Years Hence, Mother = 3 * Daughter .

Solution :-

→ Let Present age of Mother = x .

→ Let Present age of Daughter = y .

So,

→ 3 years ago , Mother was = (x - 3) years old.

→ 3 years ago , Daughter was = (y - 3) years old.

A/q,

→ Mother age = 5 * Daughter age .

→ (x - 3) = 5(y - 3)

→ x - 3 = 5y - 15

→ 5y - x = - 3 + 15

→ 5y - x = 12 ---------------------- Equation (1) .

_____________________

Similarly,

→ 2 years Hence, , Mother will be = (x + 2) years old.

→ 2 years Hence , Daughter will be = (y + 2) years old.

A/q,

→ Mother age = 3 * Daughter age .

→ (x + 2) = 3(y +2)

→ x + 2 = 3y + 6

→ x - 3y = 6 - 2

→ x - 3y = 4 ---------------------- Equation (2) .

_____________________

Adding Equation (1) & (2) we get,

→ (5y - x) + ( x - 3y) = 12 + 4

→ 5y - 3y + x - x = 16

→ 2y = 16

→ y = 8 years.

Putting This value in Equation (1) now, we get,

→ 5*8 - x = 12

→ x = 40 - 12

→ x = 28.

Hence , Present age of Mother is 28 years and her daughter is 8 years.

______________________

For One More Solution now, See Similar Question :-

https://brainly.in/question/16785350

Answer 2

The question seems a bit incorrect. Correct question:-

Three years ago the age of the mother was 5 times the age of her daughter and two years hence she will be thrice as old as her daughter will be. Find their present ages.

Given:-

• Three years ago the age of the mother was 5 times the age of her daughter.

• Two years hence she will be thrice as old as her daughter.

To find:-

The present ages of the mother and her daughter.

Solution:-

Let the present age of mother be 'x' years .

Let the present age of daughter be 'y' years .

A/q, three years ago,

5(x-3) = (y-3)

⇒5x - 15 = y - 3

⇒5x - y - 12 = 0                            ...eq.(i)

2 years hence,

3(x+2) = (y+2)

⇒3x + 6 = y + 2

⇒3x - y + 4 = 0                             ...eq.(ii)

Subtracting (i) and (ii):

  5x - y - 12 = 0                            

-

  3x - y + 4 = 0  

_____________

  2x - 16 = 0

⇒2x = 16

⇒x = 16/2

$\boxed{x=8}$

Now, putting x = 8 in eq.(i):

5x - y - 12 = 0

⇒5*8 - y = 12

⇒ -y = 12 - 40

⇒ -y = -28

$\boxed{y=28}$

So, the age of the daughter is 8 years and the age of the mother is 28 years.