Question

Question :
The age of the mother is five times that of her daughter. If 3 years ago, the age of the mother was nine times her daughter's age then, find their present ages.
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class = 8th
ch = Linear equations in one variable

Help me ! ​

Answer 1

Answer:

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,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

x=8

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

5x - y - 12 = 0

⇒5*8 - y = 12

⇒ y = 12 - 40

⇒-y = -28

y = 28

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

hope it helps

Answer 2

Step-by-step explanation:

Solution:

Let the present age of the daughter be x years, then the age of her mother is 5.x years.

• 3 years ago the age of the ughter = (x - 3) years
• The age of the mother 3 years ago =(5x-3) years

According to the given condition,

$\bf \: 5x - 3 = 9(x - 3) \\ \rightarrow 5x - 3 = 9x - 27 \\ \bf \rightarrow9x - 5x = 27 - 3 \\ \bf \rightarrow4x = 24 \\ \bf \: \rightarrow x = 6$

$\purple{ \bf \therefore \: the \: present \: age \: of \: the \: daughter = 6 \: years \: } \\ \purple{ \bf \: and \: the \: age \: of \: the \: mother \: = 5x = 30years .}$

Hope it helps you sis ✌️