Question

(ii) The sum of the present ages of mother and her daughter is 50 years. After 20 years, mother's age will be twice her daughter's age at that time. Find their present ages.​

Answer 1

Answer:

mother 40, daughter 10

Step-by-step explanation:

let daughter's age be x years

mother's present age= 50-x

AFTER 20 YEARS

Daughter's age=x+20

Mother's age=(50-x)+20   =   70-x

ACCORDING TO THE QUESTION,

mother's age = 2 * daughter's age

=> 70-x = 2*(x+20)

=>70-x = 2x + 40

=> 3x=30

=>x=10

Thus Daughter's age = 10 yrs and mother's age = 40 yrs

Answer 2

Answer

Present age of mother is 40 years and her daughter is 10 years.

$\rule{100}2$

Explanation

Let the present age of mother be M years and her daughter be D years.

Condition 1)

The sum of the present ages of mother and her daughter is 50 years.

$\implies\:\sf{M\:+\:D\:=\:50}$

$\implies\:\sf{M\:=\:50\:-\:D}$ ---- [1]

Condition 2)

After 20 years, mother's age will be twice her daughter's age at that time.

Now,

• Age of mother = (M + 20) years
• Age of daughter = (D + 20) years

Mother will be two times of her daughter.

i.e.

$\implies\:\sf{M\:+\:20\:=\:2(D\:+\:20)}$

$\implies\:\sf{M\:+\:20\:=\:2D\:+\:40}$

$\implies\:\sf{50\:-\:D\:+\:20\:=\:2D\:+\:40}$ [From (1)]

$\implies\:\sf{70\:-\:D\:=\:2D\:+\:40}$

$\implies\:\sf{2D\:+\:D\:=\:70\:-\:40}$

$\implies\:\sf{3D\:=\:30}$

$\implies\:\sf{D\:=\:10}$

•°• Present age of daughter is 10 years.

Substitute value of D = 10 in equation (1)

$\implies\:\sf{M\:=\:50\:-\:10}$

$\implies\:\sf{M\:=\:40}$

•°• Present age of mother is 40 years.

$\rule{200}2$

Verification:-

Sum of ages of both mother and her daughter is 50 years.

From above calculations -

• Present age of mother is 40 years
• Present age of her daughter is 10 years

→ 40 + 10 = 50

→ 50 = 50