How to get id of Max value

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MySQL

I want the max Average value and its id grouped by month,

Select FK_Transporter,Month, MAX(avg_rate) as BTPercent
FROM (
    SELECT kpi.FK_Transporter ,kpi.`Month`, AVG(kpi.OnTimeDelivery) as avg_rate
    FROM primarykpi as kpi,transporter as t
		WHERE kpi.FK_Transporter=t.Id and YEAR(kpi.`Month`)=2016
    GROUP BY FK_Transporter, MONTH(kpi.Month)) tp
GROUP BY tp.`Month`

This query gave me right average but id is incorrect. Couldn't able to fing the mistake .Here is output of this query

FK_Transporter       Month             MaxAvg
1	                 2016-01-01	       2.270109534263611
1	                 2016-02-01	       0.8539329767227173
1	                 2016-03-01	       0.6764709949493408

FK_transporter is 1 in all records whch is wrong . How can i fix this. Thanks.