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Byju's Answer
Standard VI
Mathematics
Finding the Value of an Expression
The number of...
Question
The number of ordered pairs (x,y) of positive integers satisfying the equation 1/x + 1/y = 1/20 is
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Solution
1
x
+
1
y
=
1
20
(
x
,
y
≠
0
)
1
x
=
1
20
-
1
y
⇒
1
x
=
y
-
20
20
y
⇒
x
=
20
y
y
-
20
Therefore
,
for
x
to
be
positive
,
y
>
20
Starting
with
y
=
21
x
=
20
(
21
)
=
420
for
y
=
22
x
=
10
(
22
)
=
220
for
y
=
23
,
x
is
not
an
integer
for
y
=
24
,
x
=
5
(
24
)
=
120
for
y
=
25
,
x
=
(
4
)
25
=
100
for
y
=
26
,
27
,
29
x
is
not
an
integer
for
y
=
28
,
x
=
70
for
y
=
30
,
x
=
60
for
y
=
31
,
32
,
33
,
34
,
35
x
is
not
an
integer
for
y
=
36
,
x
=
45
for
y
=
37
,
38
,
39
x
is
not
an
integer
for
y
=
40
,
x
=
40
Since
the
equation
is
symmetric
w
.
r
.
t
x
and
y
,
the
reverse
will
be
true
if
we
start
with
assuming
x
(
as
we
did
for
y
)
So
possible
values
of
x
(
or
y
)
are
=
21
,
22
,
24
,
25
,
28
,
30
,
36
,
40
,
45
,
60
,
70
,
100
,
120
,
220
,
420
so
total
pairs
possible
=
15
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1
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