The ratio of the present ages of a mother and har daughter is 9:2. After 4 year the ratio of thier ages will be 10:3. From the pair of linear equation variables.
Answers
Solution :-
Let the present ages of mother and her daughter be 9x years and 2x years respectively.
After 4 years,
Mother's age = (9x + 4) years
Daughter's age = (2x + 4) years
According to the question,
=> (9x + 4)/(2x + 4) = 10/3
=> 3(9x + 4) = 10(2x + 4)
=> 27x + 12 = 20x + 40
=> 27x - 20x = 40 - 12
=> 7x = 28
=> x = 28/7 = 4
Therefore,
9x = 9 × 4 = 36 years
2x = 2 × 4 = 8 years
Answer : Present age of Mother = 36 years
Daughter's age = 8 years
LINEAR EQUATIONS IN TWO VARIABLES :
Let the present age of daughter be x year and mother be y years.
Then, Ratio => 9:2 = y : x
9/2 = y/x
9x = 2y
9x/2 = y --> ( i )
After 4 years, Ratio of their ages = 10 : 3
( y + 4 ) / ( x + 4 ) = 10/3
3y + 12 = 10x + 40
3 ( 9/2) x + 12 = 10x + 40 [ From ( i ) ]
27x/2 - 10x = 40 - 12
( 27 - 20) x/2 = 28
7x/2 = 28
x = 8 years.
Putting value of 'x' in equation ( i ),
y = 9× 8/2
y = 36 years.
Present age of daughter = 8 years.
Present age of mother = 36 years.