Question

Ten years ago, the age of mother was three times the age of her son. After ten years, mother’s age will be twice that of his son. Find the ratio of their present ages ?​

Answer 1

Answer

Given:

•Ten years ago, the age of mother was three times the age of her son.

•After ten years, mother’s age will be twice that of his son

To find:

•The ratio of their present ages.

Solution:

Let the present age of Mother be x years.

Let the present age of Son be y years

As per first condition:

Ten years ago, the age of mother was three times the age of her son.

Ages 10 years ago :-

Mother = x - 10 years

Son = y - 10 years

Representing the condition mathematically.

=> x - 10 = 3 ( y - 10)

=> x - 10 = 3y - 30

=> x - 3y = - 30 + 10

=> x - 3y = -20----->1

As per second condition:

•After ten years, mother’s age will be twice that of his son

Ages after 10 years :-

Mother = x + 10 years

Son = y + 10 years

Representing the condition mathematically.

=> x + 10 = 2 ( y + 10)

=> x + 10 = 2y + 20

=> x - 2y = 20 - 10

=> x - 2y = 10 ----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Subtract equation 2 from equation 1,

...+ x - 3y = - 20

- (+ x - 2y = 10)

--------------------------

- y = - 30

y = 30

Substitute y = 30 in equation 1,

=> x - 3y = - 20

=> x - 3 ( 30) = - 20

=> x - 90 = - 20

=> x = 70

Present age of Mother = x = 70 years

Present age of Son = y = 30years

To find the ratio of the present age of Mother and Son,

=>ratio=x/y

=> ratio=70/30

=>ratio=35/15

=>ratio=7/3

•°• Ratio of the present ages of mother and son = 7 : 3

Answer 2

Answer:

hlo

your answer is here !

Step-by-step explanation:

Let the son's present age be x

So 10 yrs ago son's age = x - 10

Given that age of mother ten years ago was 3 times of son

=> mother's age 10 yrs ago = 3(x - 10)

= 3x - 30

After 10 yrs, son's age would be x + 10

Given after ten yrs, mother's age would be twice of the son

=> mother's age = 2(x + 10)

= 2x + 20

But 10 yrs ago of present time, her age was 3x - 30

So it will take 20 yrs to go 10 yrs in future from the present age.

=> 3x - 30 + 20 = 2x + 20

=> 3x - 10 = 2x + 20

=> 3x = 2x + 20 + 10

=> 3x - 2x = 30

=> x = 30.

Present age of son = 30 yrs.

=> 10 yrs ago mother's age =

3x - 30

= 3(30) - 30

=> 90 - 30

= 60 yrs.

So present age of mother = 60 + 10 = 70 yrs

Ratio =

mother : son

= 70 : 30

= 7: 3

Hope you understand

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