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ICSE Class X Math 2014 Paper

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Question : 41 of 52
Marks: +1, -0
If (x−9):(3x+6)(x-9):(3x+6) is the duplicate ratio of 4 : 9 , find the value of xx .
Solution:  
Given :(x−9):(3x+6):(x-9):(3x+6) is the duplicate ratio of 4:94:9
⇒    x−93x+6  =(  49)2\Rightarrow\;\; \frac{x-9}{3x+6}\; = \left(\;\frac{4}{9}\right)^2
⇒    x−93x+6  =  1681\Rightarrow\;\; \frac{x-9}{3x+6}\; = \;\frac{16}{81}
⇒81x−729  =48x+96\Rightarrow 81x-729\;=48x+96
⇒  81x−48x  =96+729\Rightarrow\; 81x-48x\;=96+729
⇒  33x  =825\Rightarrow\; 33x\;=825
⇒  x  =  82533=25\Rightarrow\; x\;=\;\frac{825}{33}=25
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