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please tell me which one of the following is correct
we will revert to you soon after a decision is taken in this matter.
we will revert back to you soon after a decision is taken on this issue.
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I don't think either is correct, but I may be wrong.
Try;
We will contact to you soon after a decision is taken in this matter.
We will get back to you soon after a decision is taken on this issue.
REVERT means
1 Return to a former condition, habit or type.
2 Return to a subject of discussion or thought.
Maybe you could say, 'We will revert to discussion with you soon after a decision is taken on this matter'
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Comments  

we will revert to you soon after a decision is taken in this matter.

we will revert back to you soon after a decision is taken on this issue