Question

Find the fraction such that,if its numerator is diminished by unity,it reduces to 1/2and becomes equal to 2 when the numerator is increased by 5 and the denominator is diminished by 6.

Answer 1

Let the fraction be x/y.
Here,
x-1/y = 1/2
or, 2x - 2 = y
x+5/y-6 = 2
or, x + 5 = 2y -12
Thus, x + 5 = 2(2x - 2) - 12
or, x + 5 = 4x - 16
3x = 21
x = 7
and y = 14 - 2 = 12
Thus, the fraction is 7/12.