Question

The sum of the ages of the mother and daughter is 45 years. When the age if the daughter will be equal to the present age of the mother, the sum of their ages will be 95 years. Find the present ages of the mother and her daughter.
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Answer 1

Step-by-step explanation:

Given that:The sum of the ages of the mother and daughter is 45 years. When the age if the daughter will be equal to the present age of the mother, the sum of their ages will be 95 years.

To find:Find the present ages of the mother and her daughter.

Solution:

Let the present age of mother is x years and her daughter is y years.

According to the question sum of both edges are 45 years.

$\bold{x + y = 45 }\: \: \: ...eq1$

Present age of mother in terms of daughter's age

$(45 - y) \: years$

Age difference between both the ages (y-x) years

Thus after (y-x) years hence both will grow up by (y-x) years

Age of mother-age of daughter

$= 45 - y - y \\ \\ = 45 - 2y \: \: years$

Age of daughter after 45-2y years will be:

$= 45 - 2y + y \\ \\ = 45 - y ...eq1$

Age of mother after 45-2y years

$= x + 45 - 2y \\ \\ = 45 - y + 45 - 2y \\ \\ = 90 - 3y...eq2$

ATQ

From eq1 and eq2

$45 - y + 90 - 3y = 95 \\ \\ 135 - 4y = 95 \\ \\ - 4y = 95 - 135 \\ \\ 4y = 40 \\ \\ y = 10 \: \: years$

Thus,

Age of mother will be

$45 - 10 \\ \\ = 35 \: \: years$

Thus,

Present age of daughter is 10 years and mother is 35 years.

Verification:

$10 + 35 = 45$

And when daughter will be 35 years old,mother will be (35+25)=60 years old

$35 + 60 = 95 \: \: years$

Hence proved.

Hope it helps you.

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Answer 2

Answer:

Present age of daughter is 10 years and mother is 35 years.