a father tells his daughter five years ago,i was five times as old as you. and four years from now,i shall be three times as old as you will be
Answers
Answer:
50 years and 14 years .
Step-by-step explanation:
Let the present age of father be x year .
And present age of daughter be y year .
Five year ago :
Father was 5 times old than his daughter :
( x - 5 ) = 5 ( y - 5 )
5 y - 25 = x - 5
x = 5 y - 20 ... ( i )
Four year hence :
He will be three times than his daughter
x + 4 = 3 ( y + 4 )
x + 4 = 3 y + 12
x = 3 y + 8
From ( i ) and ( ii ) we get
5 y - 20 = 3 y + 8
2 y = 28
y = 14
Putting y = 12 in ( i ) we get
x = 5 y - 20
x = 70 - 20
x = 50 .
Thus the present age of father is 50 years and his daughter 14 years .
Verification :
Five year ago he was five times .
45 = 9.
5 ( 9 ) = 9
Verified .
ANSWER:-
Given:
A father tells his daughter five years ago, I was five times as old as you. And four years from now.
To find:
Find the current ages.
Solution:
Let the current age of father be x years.
& let the current age of father's daughter be y years.
Therefore,
Five years ago:
Age of father= x- 5
Age of father's daughter= y-5
Father was five times as old as father's daughter;
=) (x-5) =5(y-5)
=) (x-5) = 5y-25
=) x-5 - 5y + 25= 0
=) x - 5y +20= 0..............(1)
Four years later:
Age of father = x+4
Age of father's daughter= y+4
Father will be three times as father's daughter;
=) (x+4) = 3(y+4)
=) (x+4) = 3y +12
=) x+4 -3y -12= 0
=) x -3y - 8= 0................(2)
So,
Using by elimination method, we get:
From equation (1) ;
x - 5y +20 = 0
=) x- 5y = -20
=) x = -20+5y...............(3)
Now,
Putting the value of x in equation (2),we get;
=) -20 +5y - 3y -8 = 0
=) -28 + 2y = 0
=) 2y = 28
=) y = 28/2
=) y = 14 years
Substituting the value of y in eq.(3), we get;
=) x = -20 + 5y
=) x= -20 + 5(14)
=) x = -20 + 70
=) x= 50 years
Hence,
Father age is, x = 50 years
father's daughter age is, y= 14 years.
Five years ago:
Age of father = x- 5
=) (50-5) years
=) 45 years
Age of father's daughter= y -5
=) (14- 5) years
=) 9 years.
And,
Three years later:
Age of father= x +4
=) (50 + 4) years
=) 54 years
Age of father's daughter=y +4
=) (14+ 4) years