1) The sum of the ages of the mother and
her daughter is 45 years. When the
age of 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.
Answers
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.
\begin{gathered}\bold{x + y = 45 }\: \: \: ...eq1 \\ \end{gathered}
x+y=45...eq1
Present age of mother in terms of daughter's age
\begin{gathered}(45 - y) \: years \\ \end{gathered}
(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
\begin{gathered} = 45 - y - y \\ \\ = 45 - 2y \: \: years \\ \\ \end{gathered}
=45−y−y
=45−2yyears
Age of daughter after 45-2y years will be:
\begin{gathered} = 45 - 2y + y \\ \\ = 45 - y ...eq1 \\ \\ \end{gathered}
=45−2y+y
=45−y...eq1
Age of mother after 45-2y years
\begin{gathered} = x + 45 - 2y \\ \\ = 45 - y + 45 - 2y \\ \\ = 90 - 3y...eq2 \\ \\ \end{gathered}
=x+45−2y
=45−y+45−2y
=90−3y...eq2
ATQ
From eq1 and eq2
\begin{gathered}45 - y + 90 - 3y = 95 \\ \\ 135 - 4y = 95 \\ \\ - 4y = 95 - 135 \\ \\ 4y = 40 \\ \\ y = 10 \: \: years \\ \\ \end{gathered}
45−y+90−3y=95
135−4y=95
−4y=95−135
4y=40
y=10years
Thus,
Age of mother will be
\begin{gathered}45 - 10 \\ \\ = 35 \: \: years \\ \\ \end{gathered}
45−10
=35years
Thus,
Present age of daughter is 10 years and mother is 35 years.
Verification:
\begin{gathered}10 + 35 = 45 \\ \\ \end{gathered}
10+35=45
And when daughter will be 35 years old,mother will be (35+25)=60 years old
\begin{gathered}35 + 60 = 95 \: \: years \\ \\ \end{gathered}
35+60=95years
Hence proved.
Hope it helps you.