Question

Five years ago the mother’s age was five times the child’s age. Now the age of the mother is three times the age of the child, what is the child’s current age? *​

Answer 1

Answer:

Let mother present age is x & daughter present age is y.

5+x=3(y+5) …………(1)

and 5 years ago

x−5=7(y−5) ……….(2)

5+x=3y+15

(−)x−5=7y−35

___________________

10=−4y+50

4y=40

y=10

from (1)

5+x=3(y+5)

5+x=3(10+5)

5+x=45

x=40

Answer 2

GIVEN :-

• Five years ago the mother’s age was five times the child’s age

• mother’s age was five times the child’s age. Now the age of the mother is three times the age of the child

TO FIND :-

• current age of child

SOLUTION :-

let mother's age be x years

and child's age be y years

now , according to the question :-

5 years ago ,

$\implies \rm{ x - 5 = 5 \: (y - 5)}$

$\implies \rm{ x - 5 = 5 \: y - 25}$

$\implies \rm{ x - 5y = 5 \: - 25}$

$\implies \rm{ \bf{x - 5y = \: - 20} \: \: \: \: \: \: \: }(1)$

now ,

$\implies \rm{ \bf{ x = \: 3y}} \: \: \: \: \: \: \: \: (2)$

BY SUBSTITUTION METHOD ,

putting value of x in eq 1

$\implies \rm{ x - 5y = \: - 20}$

$\implies \rm{ 3y- 5y = \: - 20}$

$\implies \rm{ - 2y = \: - 20}$

$\implies \boxed{ \rm{ y = \: 10}}$

now put the value of y in eq 2

$\implies \rm{ x = \: 3y}$

$\implies \rm{ x = \: 3(10)}$

$\implies \boxed{ \rm{ x = \: 30}}$

HENCE,

CURRENT AGE OF CHILD = 10 YRS

CURRENT AFE OF MOTHER = 30 YRS