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
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Step-by-step explanation:
Ans.-4/7
Let the numerator be x and denominator be y.
Let the fraction be
y
x
x+y+3=2y
(or) x−y=−3
(or) x=y−3 _____ (1)
Also ,
y−1
x−1
=
2
1
x−1=
2
y−1
x=
2
y−1
+1⇒2x=y−1+2=y+1
(or) 2x−y=1 _____ (2)
substituting (1) in (2),
2(y−3)−y=1
⇒2y−6−y=1⇒y=7
put y=7 in (1) we get x=7−3=4
∴x=4,y=7
∴ the fraction is
y
x
=
7
4
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