Ex.2
At present the age of father is 5 (Y) times that of
the age of his son. After 3 (t) years, the
father’s age would be 4 (x) times the age of his son. Find the present
ages of the father and the son?
Solution by conventional method
Let the present age of son = x yrs.
then, the present age of father = 5x yrs.
After, 3 years,
4(x+3) = 5x+3
or, 4x+12=5x-3
x = 9 yrs.
So, the son's age is 9 yrs.
Father's age = 45 yrs.
Shortcut Method:
Son's age = t(x-1) / (x-y)
The value of x can be identified easily as it will be given it the same sentence where you find value of t.
In the above formula the denominator must results in a positive value. If you think the value will come negative then reverse the denominator as (y-x)
I mean you have to always subtract the greater no. from the smaller no. so that the value obtained is always positive.
In the above example
t= 3 yrs.
x = 4
y= 5
Putting the values in the above equation
Son’s age = 3 (4-1) / 5-4
=9
and father’s age = 45 yrs.
Ex-3
Three years (t1) earlier
the father was 7 times (x) as old as his
son. Three years (t2) hence, the father’s age would be 4
times (z)
that of his son. What is the present age of the son?
Solution by conventional method
Let the present age of son = x yrs.
then, the present age of father = y yrs.
3 years earlier,
7(x-3) =y-3
or, 7x-y=18 ………. (1)
After, 3 years,
4(x+3) = y+3
or, 4x+12=y+3
or, 4x-y=-9………...(2)
Solving (1) and (2) we get, x = 9 yrs. and y = 45 yrs.
Shortcut Method
Son’s age = [t2 (z-1) + t1 (x-1)]/ (x-z)
= [3(4-1) + 3(7-1)]/ (7-4)
= (9+18)/3
= 27/3
= 9
Try yourself:
1. The age of a man is 4 times that of his son. Five years
ago the man was 9 times as old as his son was at that time. What is the present
age of the man? (Answer- 42 yrs.)
2. After 5 years the age of a father will be thrice the age
of his son, whereas 5 years ago, he was 7 times as old as his son was. What are
their present ages? (Son’s age=10 yrs. and Father’s age= 40 yrs.)
If you have any doubt/suggestion, feel free to ask in the below comment box.
