Question

five years ago,a mother was seven time as old as her daughter. Five years hence, she will be three times as old as her daughter . find their present ages​

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Present age of the daughter be 'p'

Now,

Five years ago,

Daughter age = p - 5

${\boxed{\sf\:{Mother\;Age}}}$

= 7(p - 5)

= 7p - 35

Present Age

${\boxed{\sf\:{Daughter\;Age}}}$

= p - 5 + 5

= p

Also,

${\boxed{\sf\:{Mother\;Age}}}$

= 7p - 35 + 5

= 7p - 30

Five years hence,

Daughter age = p + 5

${\boxed{\sf\:{Mother\;Age}}}$

= 7p - 30 + 5

= 7p - 25

Situation

After 5 years, mother will be 3(thrice) daughter's age.

7p - 25 = 3(p + 5)

7p - 25 = 3p + 15

7p - 3p = 15 + 25

4p = 40

$\tt{\rightarrow p=\dfrac{40}{4}}$

p = 10

$\Large{\boxed{\sf\:{Present\;Age\;of\;Daughter}}}$

p = 10 years

$\Large{\boxed{\sf\:{Present\;Age\;of\;Mother}}}$

= 7p - 30

= 7(10) - 30

= 70 - 30

= 40 years

Answer 2

Let the daughters age be x

Before 5 years:-

Mother's age = 7 (x-5)

Daughters age =x-5

At present age:-

Daughters age = x - 5 +5= x

Mother's age = 7x - 5 + 5=7x-30

Five years hence:-

Daughters age=x+5

Mother's age = 7x-30+5=7x-25

According to question:-

After 5 years mother will be thrice of daughter's age:-

7x-25=3(x+5)

7x-25=3x+15

7x-3x=15+25

4x=40

X=10

Answer:- so, daughters age =x=10years

Mother's age =7x-30=40 years

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