The numerator of a rational number is 4 less than it's denominator. If the numberator is increased by 2 and the denominator is increased by 1, then the denominator is eight times the numberator. Find the number
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Let the denominator of the rational no. be x.
Then, numerator (n)=x−4
Add 1 to both numerator and denominator,
Denominator = x+1 and Numerator =x−4+1=x−3
⟹
x+1
x−3
=
8
1
⟹8x−24=x+1
⟹7x=25
x=
7
25
Numerator =
7
25
−4=
7
25−28
=
7
−3
Rational number =
7
−3
×
25
7
=
25
−3
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