Shortcuts for Age based problems

Have a look at the following questions

Ex.1 The ages of the father three years ago was 7 times the age of his son. At present the father's age is five times that of his son? what are 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.
3 years ago,
7(x-3) = 5x-3
or, 7x-21=5x-3
or, 2x=18  
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
In the above example
t= 3 yrs.
X = 7
Y = 5
Putting the values in the above equation
Son’s age = 3 (7-1) / 7-5
= 18/2
=9
And father’s age = 45 yrs.

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