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Find In ratio and proportion, if a/b=c/d=e/f then prove that (2a+3c-4e)/(2b+3d-4f)=(5a-4c+3e)/(5b-4d+3f)

Solution:
Your problem `->` In ratio and proportion, if a/b=c/d=e/f then prove that (2a+3c-4e)/(2b+3d-4f)=(5a-4c+3e)/(5b-4d+3f)


`a/b=c/d=e/f`

Suppose, `a/b=c/d=e/f=k` (say)

`:. a=bk,c=dk,e=fk`

Now LHS`=(2a+3c-4e)/(2b+3d-4f)`

`=(2bk+3dk-4fk)/(2b+3d-4f)`

`=(k(2b+3d-4f))/(2b+3d-4f)`

`"Now cancel the common factor "(2b+3d-4f)`

`=k`

Now RHS`=(5a-4c+3e)/(5b-4d+3f)`

`=(5bk-4dk+3fk)/(5b-4d+3f)`

`=(k(5b-4d+3f))/(5b-4d+3f)`

`"Now cancel the common factor "(5b-4d+3f)`

`=k`






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