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

Answer 1

HEYA!!
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Let the present age of mother be X years

Let the present age of daughter be Y years

Ages three years ago ,
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( X - 3 ). = 5 ( Y - 3 )

X - 3 = 5 Y - 15

X - 5 Y + 12 = 0 .........................(1)


Ages two years hence ,
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( X + 2 ). = 3 ( Y + 2 )

X + 2 = 3Y + 6

X - 3Y - 4 = 0 ..................(2)



X - 3Y - 4 =0
X - 5Y + 12 = 0

- + -

2Y - 16 = 0

2Y = 16

Y = 8


Put Y = 8 in (2)

X - 24 - 4 = 0

X - 28 = 0

X = 28


☑Age of Mother is 28 years

☑Age of daughter is 8 years.


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Answer 2

Given:

Age of mother three years ago=5 times the age of daughter

Age of mother two years hence= 3 times the age of daughter

To find:

Present ages of the mother and daughter

Solution:

We can find the solution by following the given process-

Let the present age of the mother be M years and the present age of the daughter be D years.

According to the question,

Mother's age three years ago is 5 times the age of daughter

So, (M-3)=5(D-3)

M-3=5D-15

M-5D= -12 (Equation 1)

Similarly, two years hence, she will be thrice as old as her daughter.

So, (M+2)=3(D+2)

M+2=3D+6

M-3D=4 (Equation 2)

Using the Elimination method, we will solve the two equations

M-5D= -12

M-3D=4

On subtracting,

-2D= -16

D=8 years

So, M= 28 years

Therefore, the present ages of the mother and daughter are 28 and 8 years, respectively.