# The sum of numerator and denominator of fraction is 3 less than twice the denominator.if the numerator and denominator are decreased by 1 the numerator becomes half denominator determine fraction

Let the numerator be x and the denominator be y

Sum of numerator and denominator = x + y

Given x + y is 3 less than twice the denominator

So,

=> x + y = 2y - 3

=> x - y +3 = 0      ...(1)

Also, if numerator and denominator are decreased by 1, The numerator becomes half of the denominator

=>(x-1) = 1/2(y-1)

2x - 2 = y – 1

2x - y =2 -1 =1

2x - y = 1      ....(2)

Subtracting (2) and (1) gives x - y + 3 - (2x - y - 1) = 0

x - y + 3 – 2x + y + 1 = 0

-x + 4 =0

x = 4

Substituting x value in (1) gives 4 - y + 3 = 0

y = 7

Therefore x = 4 and y = 7;

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