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Byju's Answer
Standard X
Mathematics
Elimination Method of Finding Solution of a Pair of Linear Equations
A fraction be...
Question
A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.
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Solution
Let the numerator of the fraction be x and the denominator be y.
According to the question,
x
-
2
y
=
1
3
.
.
.
(
i
)
and
x
y
-
1
=
1
2
.
.
.
(
ii
)
Solving
equation
i
,
we
get
3
x
-
2
=
y
⇒
3
x
-
6
=
y
.
.
.
iii
Substituting
the
value
of
y
in
equation
ii
,
we
get
x
3
x
-
6
-
1
=
1
2
⇒
2
x
=
3
x
-
6
-
1
⇒
2
x
=
3
x
-
7
⇒
2
x
-
3
x
=
-
7
⇒
-
x
=
-
7
⇒
x
=
7
.
.
.
(
iv
)
From
(
iii
)
and
(
iv
)
,
we
get
x
=
7
and
y
=
15
Hence
,
the
fraction
is
7
15
.
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