Shortcut:
If t_{1} years earlier the age of the father was 'q' times the age of his son. t_{2} years hence, the age of the father becomes 'n' times the age of his son. Then
The present age of the son =
t_{2}(n − 1) + t_{1}(q − 1)
/
q − n
and
The present age of the father = [
son's age
/
2
(n + q) −
t_{1}
/
2
(q − 1) +
t_{2}
/
2
(n − 1)] years respectively.
if t_{1} = t_{2} = t, then the
Son's present age =
t(q + n − 2)
/
q − n
and
Father's present age = [
son's age
/
2
(q + n) −
t
/
2
(q − n) ]
One year ago Dinesh's age was
4
/
3
of Zahir's age.
One year hence Dinesh's age will be
5
/
4
of Zahir's age.
So, t_{1} = t_{2} = 1, q =
4
/
3
, n =
5
/
4
Using these values in the shortcut, we get:
Zahir's present age =
1(4/3 + 5/4 − 2)
/
4/3 − 5/4
=
(16 + 15 − 24)/12
/
(16 − 15)/12
=
(31 − 24)/12
/
1/12
=
7/12
/
1/12
=
7 x 12
/
12
= 7
Hence, age of Zahir is 7 years.
Now, by the first relation:
D − 1
/
7 − 1
=
4
/
3
D − 1
/
6
=
4
/
3
D − 1 = 6 x
4
/
3
D = 8 + 1 = 9
Dinesh age is 9 years.
Sum of Dinesh & Zahir age is (9 + 7) years = 16 years
