Let the age of two sisters x and y (Let us assume that y is younger sister).
Since sum of the age of two sisters is 31, So x + y = 31
x + y = 31 ............(1)
Five years ago:
The age of two sisters x - 5 and y - 5
y - 5 = (x - 5) - 3
y - 5 = x - 8
or y = x - 3 ....(2)
Substitute the value of y in equation (1)
x + x - 3 = 31
2x = 34
or x = 17
Again substitute the value of x in equation (2)
y = 17 - 3 = 14
Therefore both the sisters are of 14 and 17.
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