Question

the sum of present age of mother and her daughter is 31 yaers.3 yaer ago the of mother is 4 time of her daughter of that time.the find thair present ages​

Answer 1

Answer:

Sum of ages = 50.

let mothers age be x

and daughters age (50-x)

After 20 years:

Mothers age x + 20

Daughters age (50 - x) + 20

given mothers age = 2× daughters age

x + 20 = 2 (50 - x + 20)

x + 20 = 100 - 2x + 40

3x = 120

x = 40

therefore mothers age 40 yrs. Daughters age 10 yrs.

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Step-by-step explanation:

Answer 2

Given :

Sum of present ages : 31 years

Mother's age is 4 times her daughter, before 3 years.

To find :

The present ages of mother and daughter.

Solution :

First, we should find the sum of their ages before 3 years.

Sum of ages (3 years ago) :

$\sf \dashrightarrow 31 - (3 + 3)$

$\sf \dashrightarrow 31 - 6$

$\sf \dashrightarrow 25 \: years$

Now, we can find the ages of mother and daughter, 3 years ago.

Daughter's age (3 years ago) :

$\sf \dashrightarrow Daughter's age + Mother's age = 25$

$\sf \dashrightarrow y + 3y = 25$

$\sf \dashrightarrow 4y = 25$

$\sf \dashrightarrow y = \dfrac{25}{4}$

$\sf \dashrightarrow y = 6.25$

Now, we can find the age of mother, 3 years ago.

Mother's age (3 years ago) :

$\sf \dashrightarrow 3y = 3(6.25)$

$\sf \dashrightarrow 18.75 \: years$

Now, we can find the present ages of mother and daughter.

Present age of daughter :

$\sf \dashrightarrow 6.25 + 3$

$\sf \dashrightarrow 9.25 \: years$

$\sf \dashrightarrow 9 \: years \: 3 \: months$

Present age of mother :

$\sf \dashrightarrow 18.75 + 3$

$\sf \dashrightarrow 21.75 \: years$

$\sf \dashrightarrow 21 \: years \: 9 \: months$

Hence, the present ages of daughter and mother are 9.25 and 21.75 years respectively.