Reciprocals
This part deals with reciprocals. Using the method explained below many such problems can be solved merely by mental calculation alone.
Let us consider
x + 1 = 10
x 3
Under the usual method, we cross multiply to obtain a quadratic equation which is then solved to obtain 'x'.
But by Vilokanam sutra of Vedic mathematics, the problem can be solved merely at a glance by simple mental calculation.
10/3 can be written as 3 + 1/3
Therefore x + 1 = 3 + 1
x 3
==> x = 3 or 1/3
Similarly,
2) x + 1 = 37 = 6 + 1
x 6 6
Therefore from the sutra we have x = 6 or 1/6
3) 1 + x + 1 = 26 = 5 + 1
x + 1 1 5 5
Therefore from the sutra we have x + 1 = 5 or 1/5
==> x = 4 or -4/5
4) x - 3 + x + 3 = 5 = 2 + 1
x + 3 x - 3 2 2
Therefore we have x - 3 = 2 or 1
x + 3 2
==> x = -9 or 9
5) x + 1 = 13
x 6
Here 13/6 can be split up into 2/3 + 3/2
Therefore x + 1 = 2 + 3
x 3 2
==> x = 2/3 or 3/2
6) x + x + 1 = 25 = 3 + 4
x + 1 x 12 4 3
==> x = 4 or 3
x + 1 3 4
==> x = -4 or 3
7) x - 1 = 5 = 3 - 2
x 6 2 3
Therefore x = 3/2 or -2/3
8) x - x + 2 = 15 = 8 - 7
x + 2 x 56 7 8
==> x = 8 or -7
x + 2 7 2
==> x = -16 or -14/9