2 years ago your mother was four times as old as her daughter 8 year hence mother's age will exceed her daughter age by 12 years the ratio of present age of mother and daughter is
Answers
Answer:
The ratio of present ages of mother and daughter is 3 : 1.
Step-by-step explanation:
Let,
Daughter's age, 2 years ago, was a years
Mother's age, 2 years ago, was 4a years [ 4 times of a years or daughter's age ]
Therefore,
Present age of daughter = ( a + 2 ) years
Present age of mother = ( 4a + 2 ) years
After 8 years, ages will be increased by 8 years :
Age of daughter after 8 years = ( a + 2 + 8 ) years = ( a + 10 ) years
Age of mother after 8 years = ( 4a + 2 + 8 ) years = ( 4a + 10 ) years
According to the question : -
= > Mother's age will exceed daughter's age by 12 years
= > ( 4a + 10 ) years = ( a + 10 ) years + 12 years
= > 4a + 10 = a + 10 + 12
= > 4a + 10 = a + 10 + 12
= > 4a - a + 10 - 10 = 12
= > 3a = 1 2
= > a = 12 / 3
= > a = 4
Hence,
Ratio of present of mother and daughter = ( present age of mother or 4a + 2 years ) : ( present age of daughter or a + 2 years )
= > Required ratio = { 4( 4 ) + 2 } : { 4 + 2 }
= > Required rattio = { 16 + 2 } : { 6 }
= > Required ratio = 18 : 6
= > Required ratio = 3 : 1
Therefore the ratio of present ages of mother and daughter is 3 : 1.
Answer:
Step-by-step explanation:
Let the Age of Mother be "x" years.
& that of her Daughter be "y" years.
2 Years Ago,
Age of Mother = ( x-2) year.
& Daughter's Age = (y-2) years.
CONDITION |,
( x-2) = 4 ( y-2)
=> x - 2 = 4y - 8
=> x - 4y = -6 _____________(1).
CONDITION ||,
8 Year Hence,
Age of Mother = ( x+8) yrs.
& Daughter's Age = ( y+8) yrs
( x+8) = ( y+8) + 12
=> x + 8 = y + 20
=> x - y = 12
=> x = 12 + y____________(2).
Putting eq (2) in eq (1). we get,
x - 4y = -6
=> 12 + y - 4y = -6
=> - 3y = -18
=> y = 6 years.
Putting y = 6 in eq (2). we get,
x = 12 + 6 = 18 years.
Hence,
Mother's Age = 18 years.
& Daughter's Age = 6 years.
Ratio of Mother's Age to Daughter's Age = 18 : 6
= 3 : 1.