Equivalent Emf in case of polarity being changed

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I read the following statement in a book: "if polarity of m number of cells out of total n number of cells are connected in series with external resistance R is reversed then equivalent emf of such combination of cells is given by
E_eq= (n-2m)E (where, each cell has same value of emf= E"
I don't understand why we subtract 2m... Why not just m from the total number of cell. Please explain?

 

[ash64449]

it is like this:

consider we have 4 cells of equal emf e. one is reversed.. as a result.. one is cancelled.. therefore equivalent emf is 2e=(4e-2e)

similarly consider n cells... m is reversed.. m cells are cancelled... equivalent emf is (n-2m)e

 

[ash64449]

it is because one reversed polarity actually cancels 1 cell having opposite polarity.therefore both cell, the one reversed and one original polarity gets cancelled.. which means:
if m cells are reversed, then 2m cells cancels of from the equivalent.. therefore equivalent emf becomes (n-2m)e

 

[Quotes]

I got it! Thanks a lot.