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Byju's Answer
Standard X
Mathematics
Proportion
If 2 x-3 y 3 ...
Question
If
2
x
-
3
y
3
z
+
y
=
z
-
y
z
-
x
=
x
+
3
z
2
y
-
3
x
then prove that every ratio =
x
y
.
Open in App
Solution
2
x
-
3
y
3
z
+
y
=
z
-
y
z
-
x
=
x
+
3
z
2
y
-
3
x
⇒
2
x
-
3
y
3
z
+
y
=
3
z
-
y
3
z
-
x
=
x
+
3
z
2
y
-
3
x
⇒
2
x
-
3
y
3
z
+
y
=
3
z
-
y
3
z
-
x
=
x
+
3
z
2
y
-
3
x
=
2
x
-
3
y
-
3
z
-
y
+
x
+
3
z
3
z
+
y
-
3
z
-
x
+
2
y
-
3
x
Theorem
of
equal
ratios
⇒
2
x
-
3
y
3
z
+
y
=
3
z
-
y
3
z
-
x
=
x
+
3
z
2
y
-
3
x
=
2
x
-
3
y
-
3
z
+
3
y
+
x
+
3
z
3
z
+
y
-
3
z
+
3
x
+
2
y
-
3
x
⇒
2
x
-
3
y
3
z
+
y
=
3
z
-
y
3
z
-
x
=
x
+
3
z
2
y
-
3
x
=
3
x
3
y
∴
2
x
-
3
y
3
z
+
y
=
z
-
y
z
-
x
=
x
+
3
z
2
y
-
3
x
=
x
y
Suggest Corrections
1
Similar questions
Q.
If
2
x
-
3
y
3
z
+
y
=
z
-
y
z
-
x
=
x
+
3
z
2
y
-
3
x
,
then show that each ratio is
x
y
.
Q.
If
2
x
−
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y
3
z
+
y
=
z
−
y
z
−
x
=
x
+
3
z
2
y
−
3
x
then prove that every ratio
=
x
y
Q.
If
x
y
+
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-
x
=
y
z
+
x
-
y
=
z
x
+
y
-
z
and x + y + z
≠
0 then show that each ratio is equal to 1.
Q.
x
(
y
+
z
−
x
)
log
x
=
y
(
z
+
x
−
y
)
log
y
=
z
(
z
+
x
−
y
)
log
z
,
then prove that
x
y
y
x
=
z
y
y
z
=
x
z
z
x
.
Q.
Prove that
∣
∣ ∣ ∣
∣
x
y
z
x
2
y
2
z
2
y
z
z
x
x
y
∣
∣ ∣ ∣
∣
=
(
y
−
z
)
(
z
−
x
)
(
x
−
y
)
(
y
z
+
z
x
+
x
y
)
.
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