Hello, hope you are doing well!

Suppose your particle is at origin and you are applying force P and 2P from any side, and if the first force(P) is doubled it will become 2P and if second force is (2P)  is increased by 20N it will become become 2P+20N. Now the resultant would be same or unaltered only when the ratio of (P and 2P) would be equal to the ratio of (2P and 2P+20P).

That is (P/2P)=(2P/(2P+20)) => 1/2=(2P/(2P+20)) => 2P+20P=4P => 2P=20 => P=10. so, the value of P comes out to be 10N, and That is your answer.

Thank you