Two forces P and 2P act at a point. If the first force is increased by 5N and the other trebled, the direction of the resultant is not altered then find 'P'

Explanation

Given P=P,Q=2P
`P=P+5` and `Q+3(2P)=6P=3Q`
`prop=prop,theta=theta`
We know that tan `prop=(Qsintheta)/(P-Qcostheta)=(Q'sintheta')/(P'+Q'costheta')`
i.e. `(cancelQ)/(P+Qcostheta)=(3cancelQ)/(((P+5)+3Qcostheta)`
`3P+3Qcostheta=P+P+5+3Pcostheta`
2P=5
`:." "P=2.5N`