Numerator of a fraction is 1 less than the denominator . If 3 is subtracted from the numerator and denominator , the fraction obtained is 2/1 .Then the fraction is
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Class 10
>>Maths
>>Pair of Linear Equations in Two Variables
>>Algebraic Methods of Solving a Pair of Linear Equations
>>A fraction becomes 1/3 when 1 is subtrac
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A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.
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Solution
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Let the numerator =x
and the denominator =y
So, the fraction =
y
x
According to the question,
Condition I:
y
x−1
=
3
1
⇒3(x−1)=y
⇒3x−y=y
⇒3x−y−3=0 ..(i)
Condition II:
y+8
x
=
4
1
⇒4x=y+8
⇒4x−y=8
⇒4x−y−8=0...(ii)
By cross-multiplication method, we have
⇒
8−3
x
=
−12+24
y
=
−3+4
1
⇒
5
x
=
12
y
=
1
1
I II III
On taking I and III ratio, we get
⇒
5
x
=
1
1
⇒x=5
On taking II and III ratio, we get
⇒
12
y
=
1
1
⇒y=12
So, the numerator is 5 and the denominator is 12
Hence, the fraction is
12
5