Question

The numerator of a rational number is 4 less than the denominator.if 1is added to numerator and denominator both the rational number becomes 1/2.find the rational number

Answer 1

Let denominator be x
Numerator = x-4
When 1 is added:-
Denominator = x+1
Numerator= x-3
x-3/x+1=1/2
x+1=2(x-3)
x+1=2x-6
x-2x=-6-1
-x=-7
x=7
Original Numerator = x-4
= 7-4
= 3
Original Denominator = x
= 7
Original Fraction = 3/7

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Answer 2

Let the Numerator be 'x',Then Denominator=x+4
Rational No=x/x+4
Now 1 is added,
x+1/x+5
So its Given that,
x+1/x+5=2/3.
Cross multiplying on both sides,we get:
2(x+5)=3(x+1)
2x+10=3x+3
Therefore,x=7
Denominator=7+4=11
So Fraction=7/11

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