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ICSE Class X Math 2013 Paper

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Question : 4 of 46
Marks: +1, -0
What number must be added to each of the number 6, 15, 20 and 43 to make them proportional?
Solution:  
Let the number must be added be xx , then the new number =6+x,15+x,20+x,43+=6+x, 15+x, 20+x, 43+ xx
∵\because These are proportionals.
  6+x:15+x::20+x:43+x\;6+x: 15+x:: 20+x: 43+x
      (6+x)(43+x)=(15+x)(20+x)\; \;\; (6+x)(43+x)=(15+x)(20+x)
     or   258+6x+43x+x2  \;\;\text{ or }\; 258+6 x+43 x+x^2\; =300+20x+15x+x2=300+20 x+15 x+x^2
     or     49x−35x  \;\;\text{ or }\;\;49 x-35 x\; =300−258=300-258
     or     14x  =42\;\;\text{ or }\;\;14 x\;=42
     or     x  =3.\;\;\text{ or }\;\;x\;=3 .
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