Question

Five years hence, a mother's age will be three
times that of her daughter's and five years
ago, the mother was 7 times as old as the
daughter was. Find their present ages.​

Answer 1

Step-by-step explanation:

Let present age of daughter be x.

So 5 years ago her age =x−5

Her mother's age is 7(x−5)

Including 5 years from past to present and then to future =10

So 7x−35+10=3(x−5+10)

7x−25=3x+15

4x=40

x=10

so daughters age=10

mother's age=4×10=40.

Answer 2

Solution :

Let the present age of Mother's be r years.

Let the present age of Daughter's be m years.

A/q

$\underbrace{\sf{After\:5\:years\::}}}$

The age of Mother's will be (r+5) years

The age of Daughter's will be (m+5) years

$\longrightarrow\sf{r+5=3(m+5)}\\\\\longrightarrow\sf{r+5=3m+15}\\\\\longrightarrow\sf{r-3m=15-5}\\\\\longrightarrow\sf{r-3m=10...................(1)}$

$\underbrace{\sf{5\:years\:ago\::}}}$

The age of Mother's will be (r-5) years

The age of Daughter's will be (m-5) years

$\longrightarrow\sf{r-5=7(m-5)}\\\\\longrightarrow\sf{r-5=7m-35}\\\\\longrightarrow\sf{r-7m=-35+5}\\\\\longrightarrow\sf{r-7m=-30}\\\\\longrightarrow\sf{r=-30+7m.......................(2)}$

∴Putting the value of r in equation (1),we get;

$\longrightarrow\sf{-30+7m-3m=10}\\\\\longrightarrow\sf{-30+4m=10}\\\\\longrightarrow\sf{4m=10+30}\\\\\longrightarrow\sf{4m=40}\\\\\longrightarrow\sf{m=\cancel{40/4}}\\\\\longrightarrow\bf{m=10\:years}$

∴Putting the value of m in equation (2),we get;

$\longrightarrow\sf{r=-30+7(10)}\\\\\longrightarrow\sf{r=-30+70}\\\\\longrightarrow\bf{r=40\:years}$

Thus;

$\boxed{\sf{The\:present\:age\:of\:Mother's\:=r=40\:years}}}}\\\boxed{\sf{The\:present\:age\:of\:Daughter's\:=m=10\:years}}}}$